Question 11 Mark
Write true $(T)$ or false $(F)$ for the following statements.
The square of a prime number is prime.
AnswerIf $p$ is a prime number,its square is $p^2$, which has at least three factors, $1, p$ and $p^2$. Since it has more than two factors, it is not a prime number.
View full question & answer→Question 21 Mark
Using square root table, find the square root: $110$
Answer$\sqrt{110}=\sqrt{2}\times\sqrt{5}\times\sqrt{11}$ $=1.414\times2.236\times3.317$ (Using the suare root table to find all the square roots) $=10.488$
View full question & answer→Question 31 Mark
What will be the units digit of the squares of the following numbers$?$
$52698$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $8.$ Hence, the units digit is the last digit of $64 (64 = 8^2)$, which is $4.$
View full question & answer→Question 41 Mark
Write true $(T)$ or false $(F)$ for the following statements.
No square number is negative.
AnswerTrue.
Solution:
The square of a negative number will be positive because negative times negative is positive.
View full question & answer→Question 51 Mark
What will be the units digit of the squares of the following numbers$?$
$977$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $7.$ Hence, the units digit is the last digit of $49 (49 = 7^2)$, which is $9.$
View full question & answer→Question 61 Mark
Using square root table, find the square root: $7$
AnswerFrom the table, we directly find that the square root of $7$ is $2.646$
View full question & answer→Question 71 Mark
By just examining the units digits, can you tell which of the following cannot be whole squares$?$
$i. 1026$
$ii. 1028$
$iii. 1024$
$iv. 1022$
$v. 1023$
$vi. 1027$
AnswerIf the units digit of a number is $2, 3, 7$ or $8,$ the number cannot be a whole square.
$i. 1026$ has $6$ as the units digit, so it is possibly a perfect square.
$ii. 1028$ has $8$ as the units digit, so it cannot be a perfect square.
$iii. 1024$ has $4$ as the units digit, so it is possibly a perfect square.
$iv. 1022$ has $2$ as the units digit, so it cannot be a perfect square.
$v. 1023$ has $3$ as the units digit, so it cannot be a perfect square.
$vi. 1027$ has $7$ as the unit digit, so it cannot be a perfect square.
Hence, by examining the units digits, we can be certain that $1028, 1022, 1023$ and $1027$ cannot be whole squares.
View full question & answer→Question 81 Mark
Find the value of: $\frac{\sqrt{80}}{\sqrt{405}}$
AnswerWe have, $\frac{\sqrt{80}}{\sqrt{405}}=\sqrt{\frac{80}{405}}$ $=\sqrt{\frac{16}{81}}=\frac{\sqrt{16}}{\sqrt{81}}=\frac{4}{9}$
View full question & answer→Question 91 Mark
Using square root table, find the square root: $3509$
AnswerUsing the table to find $\sqrt{29}$$\sqrt{3509}=\sqrt{121}\times\sqrt{29}$
$=11\times5.3851$
$=59.235$
View full question & answer→Question 101 Mark
Write true $(T)$ or false $(F)$ for the following statements.
The product of two square numbers is a square number.
AnswerIf $a^2$ and $b^2$ are two squares, their product is $a^2$ × $b^2$ = $(a × b)^2$, which is a square.
View full question & answer→Question 111 Mark
Write true $(T)$ or false $(F)$ for the following statements. The number of digits in a square number is even.
Answer$100$ is the square of a number but its number of digits is three, which is not an even number.
View full question & answer→Question 121 Mark
What will be the units digit of the squares of the following numbers$?$
$55555$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $5 .$ Hence, the units digit is the last digit of $25(25=5^2)$, which is $5 .$
View full question & answer→Question 131 Mark
Given that, $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ evaluate each of the following: $\sqrt{\frac{2500}{3}}$
AnswerGiven, $\sqrt{3}=1.732$ $\sqrt{\frac{2500}{3}}=\frac{\sqrt{2500}}{\sqrt{3}}=\frac{50}{1.732}=28.867$
View full question & answer→Question 141 Mark
Using square root table, find the square root, $\frac{99}{144}$
Answer$\sqrt{\frac{99}{144}}=\frac{\sqrt{3\times3\times11}}{\sqrt{144}}$ $=\frac{3\sqrt{11}}{12}$ $=\frac{3\times3.3166}{12}$ $\big($Using the square root table to find $\sqrt{11}\big)$ $=0.829$
View full question & answer→Question 151 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following: $\frac{256}{5}$
AnswerFrom the given values, we can simplify the expressions in the following manner: $\sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155$
View full question & answer→Question 161 Mark
Write true $(T)$ or false $(F)$ for the following statements.
The sum of two square numbers is a square number.
AnswerFalse.
Solution:
$1$ is the square of a number $(1 = 1^2)$. But $1 + 1= 2$, which is not the square of any number.
View full question & answer→Question 171 Mark
What will be the units digit of the squares of the following numbers?
$52$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $2 .$ Hence, the units digit is $2^2$, which is equal to $4 .$
View full question & answer→Question 181 Mark
Using square root table, find the square root:
$82$
AnswerUsing the table to find $\sqrt{2}$ and $\sqrt{41}$
$\sqrt{82}=\sqrt{2}\times\sqrt{41}$
$=1.414\times6.403$
$=9.055$
View full question & answer→Question 191 Mark
Write true $(T)$ or false $(F)$ for the following statements.
The difference of two square numbers is a square number.
Answer$4$ and $1$ are squares $(4 = 2^2, 1 = 1^2)$. But $4 - 1= 3$, which is not the square of any number.
View full question & answer→Question 201 Mark
Using square root table, find the square root: $540$
AnswerUsing the table to find $\sqrt{3}$ and $\sqrt{5}$ $\sqrt{540}=\sqrt{54}\times\sqrt{10}$ $=2\times3\sqrt{3}\times\sqrt{5}$ $=2\times3\times1.732\times2.2361$ $=23.24$
View full question & answer→Question 211 Mark
Using square root table, find the square root: $74$
AnswerUsing the table to find $\sqrt{2}$ and $\sqrt{37}$
$\sqrt{74}=\sqrt{2}\times\sqrt{37}$
$=1.414\times0.083$
$=8.602$
View full question & answer→Question 221 Mark
What will be the units digit of the squares of the following numbers$?$
$99880$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $0 .$ Hence, the units digit is $0^2$, which is equal to $0 .$
View full question & answer→Question 231 Mark
What will be the units digit of the squares of the following numbers$?$
$53924$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $4 .$ Hence, the units digit is the last digit of $16\left(16=4^2\right)$, which is $6 .$
View full question & answer→Question 241 Mark
Using square root table, find the square root: $15$
AnswerUsing the table to find $\sqrt{3}$ and $\sqrt{5}$ $\sqrt{15}=\sqrt{3}\times\sqrt{5}$ $=1.732\times2.236$ $=3.873$
View full question & answer→Question 251 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following: $\frac{27}{50}$
AnswerFrom the given values, we can simplify the expressions in the following manner: $\sqrt{\frac{27}{50}}=\frac{3\sqrt{3}}{5\sqrt{2}}=\frac{3\times1.732}{5\times1.414}=0.735$
View full question & answer→Question 261 Mark
Find the value of: $\sqrt{72}\times\sqrt{338}$
AnswerWe have, $\sqrt{72}\times\sqrt{338}=\sqrt{72\times338}$ $=\sqrt{2\times2\times2\times3\times3\times2\times13\times13}$ $=\sqrt{2\times2\times2\times2\times3\times3\times13\times13}$ $=2\times2\times3\times13$ $=156$
View full question & answer→Question 271 Mark
The following numbers are not perfect squares. Give reason.
$i. 1547$
$ii. 45743$
$iii. 8948$
$iv. 333333$
AnswerA number ending with $2, 3, 7$ or $8$ cannot be a perfect square.
$i.$ Its last digit is $7.$ Hence, $1547$ cannot be a perfect square.
$ii.$ Its last digit is $3.$ Hence, $45743$ cannot be a perfect square.
$iii.$ Its last digit is $8.$ Hence, $8948$ cannot be a perfect square.
$iv.$ Its last digit is $3.$ Hence, $333333$ cannot be a perfect square.
View full question & answer→Question 281 Mark
Write true $(T)$ or false $(F)$ for the following statements.
There is no square number between $50$ and $60.$
Answer$7^2=49$ and $8^2=64.7$ and $8$ are consecutive numbers and hence there are no square numbers between $50$ and $60 .$
View full question & answer→Question 291 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following: $\frac{150}{7}$
AnswerFrom the given values, we can simplify the expressions in the following manner: $\sqrt{\frac{150}{7}}=\frac{5\sqrt{2}\times\sqrt{3}}{\sqrt{7}}$ $=\frac{5\times1.414\times1.732}{2.646}=4.628$
View full question & answer→Question 301 Mark
Write true $(T)$ or false $(F)$ for the following statements.
There are fourteen square number upto $200$.
Answer$14^2$ is equal to $196 ,$ which is below $200$. There are $14$ square numbers below $200$
View full question & answer→Question 311 Mark
Using square root table, find the square root: $198$
AnswerUsing the table to find $\sqrt{2}$ and $\sqrt{11}$ $\sqrt{198}=\sqrt{2}\times\sqrt{9}\times\sqrt{11}$ $=1.414\times3\times3.317$ $=14.070$
View full question & answer→Question 321 Mark
Using square root table, find the square root: $8700$
AnswerUsing the table to find $\sqrt{3}$ and $\sqrt{29}$ $\sqrt{8700}=\sqrt{3}\times\sqrt{29}\times\sqrt{100}$ $=1.7321\times5.385\times10$ $=93.27$
View full question & answer→Question 331 Mark
Find the value of: $\sqrt{45}\times\sqrt{20}$
AnswerWe have, $\sqrt{45}\times\sqrt{20}=\sqrt{3\times3\times5\times2\times2\times5}$ $=\sqrt{3\times3\times2\times2\times5\times5}$ $=30$
View full question & answer→Question 341 Mark
What will be the units digit of the squares of the following numbers?
$4583$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $3$. Hence, the units digit is $3^2$, which is equal to $9$.
View full question & answer→Question 351 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following: $\frac{400}{63}$
AnswerFrom the given values, we can simplify the expressions in the following manner: $\sqrt{\frac{400}{63}}=\frac{20}{3\sqrt{7}}$ $=\frac{20}{3\times2.646}=2.520$
View full question & answer→Question 361 Mark
What will be the units digit of the squares of the following numbers$?$
$12796$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $6.$ Hence, the units digit is the last digit of $36 (36 = 6^2)$, which is $6.$
View full question & answer→Question 371 Mark
Using square root table, find the square root, $\frac{57}{169}$
Answer$\sqrt{\frac{57}{169}}=\frac{\sqrt{3}\times\sqrt{19}}{\sqrt{169}}$ $=\frac{1.732\times4.3589}{13}$ $\big($ Using the square root table to find $\sqrt{3}$ and $\sqrt{19}\big)$ $=0.581$
View full question & answer→Question 381 Mark
What will be the units digit of the squares of the following numbers$?$
$78367$
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is $7.$ Hence, the units digit is the last digit of $49 (49 = 7^2)$, which is $9.$
View full question & answer→Question 391 Mark
Given that, $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ evaluate each of the following: $\sqrt{\frac{144}{7}}$
AnswerGiven, $\sqrt{7}=2.646$ $\sqrt{\frac{144}{7}}=\frac{\sqrt{144}}{\sqrt{7}}=\frac{12}{2.646}=4.536$
View full question & answer→Question 401 Mark
Using square root table, find the square root: $6929$
AnswerUsing the table to find $\sqrt{41}$$\sqrt{6929}=\sqrt{169}\times\sqrt{41}$
$=13\times6.4031$
$=83.239$
View full question & answer→Question 411 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following: $\frac{196}{75}$
AnswerFrom the given values, we can simplify the expressions in the following manner: $\sqrt{\frac{196}{75}}=\frac{14}{5\sqrt{3}}$ $=\frac{14}{5\times1.732}=1.617$
View full question & answer→Question 421 Mark
Using square root table, find the square root:
$1110$
Answer$\sqrt{1110}=\sqrt{2}\times\sqrt{3}\times\sqrt{5}\times\sqrt{37}$
$=1.414\times1.732\times2.236\times6.083$ (Using the table to find all the square roots)
$=33.312$
View full question & answer→Question 431 Mark
What will be the units digit of the squares of the following numbers?
99880
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 0. Hence, the units digit is 02, which is equal to 0.
View full question & answer→Question 441 Mark
What will be the units digit of the squares of the following numbers?
977
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 7. Hence, the units digit is the last digit of 49 (49 = 72), which is 9.
View full question & answer→Question 451 Mark
What will be the units digit of the squares of the following numbers?
78367
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 7. Hence, the units digit is the last digit of 49 (49 = 72), which is 9.
View full question & answer→Question 461 Mark
What will be the units digit of the squares of the following numbers?
55555
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 5. Hence, the units digit is the last digit of 25 (25 = 52), which is 5.
View full question & answer→Question 471 Mark
What will be the units digit of the squares of the following numbers?
53924
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 4. Hence, the units digit is the last digit of 16 (16 = 42), which is 6.
View full question & answer→Question 481 Mark
What will be the units digit of the squares of the following numbers?
52698
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 8. Hence, the units digit is the last digit of 64 (64 = 82), which is 4.
View full question & answer→Question 491 Mark
What will be the units digit of the squares of the following numbers?
52
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 2. Hence, the units digit is 22, which is equal to 4.
View full question & answer→Question 501 Mark
What will be the units digit of the squares of the following numbers?
4583
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 3. Hence, the units digit is 32, which is equal to 9.
View full question & answer→Question 511 Mark
What will be the units digit of the squares of the following numbers?
12796
AnswerThe units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 6. Hence, the units digit is the last digit of 36 (36 = 62), which is 6.
View full question & answer→Question 521 Mark
Using square root table, find the square root,
$\frac{99}{144}$
Answer$\sqrt{\frac{99}{144}}=\frac{\sqrt{3\times3\times11}}{\sqrt{144}}$
$=\frac{3\sqrt{11}}{12}$
$=\frac{3\times3.3166}{12}$ $\big($Using the square root table to find $\sqrt{11}\big)$
$=0.829$
View full question & answer→Question 531 Mark
Using square root table, find the square root,
$\frac{57}{169}$
Answer$\sqrt{\frac{57}{169}}=\frac{\sqrt{3}\times\sqrt{19}}{\sqrt{169}}$
$=\frac{1.732\times4.3589}{13}$ $\big($ Using the square root table to find $\sqrt{3}$ and $\sqrt{19}\big)$
$=0.581$
View full question & answer→Question 541 Mark
Using square root table, find the square root:
8700
AnswerUsing the table to find $\sqrt{3}$ and $\sqrt{29}$
$\sqrt{8700}=\sqrt{3}\times\sqrt{29}\times\sqrt{100}$
$=1.7321\times5.385\times10$
$=93.27$
View full question & answer→Question 551 Mark
Using square root table, find the square root:
82
AnswerUsing the table to find $\sqrt{2}$ and $\sqrt{41}$
$\sqrt{82}=\sqrt{2}\times\sqrt{41}$
$=1.414\times6.403$
$=9.055$
View full question & answer→Question 561 Mark
Using square root table, find the square root:
74
AnswerUsing the table to find $\sqrt{2}$ and $\sqrt{37}$
$\sqrt{74}=\sqrt{2}\times\sqrt{37}$
$=1.414\times0.083$
$=8.602$
View full question & answer→Question 571 Mark
Using square root table, find the square root:
7
AnswerFrom the table, we directly find that the square root of 7 is 2.646
View full question & answer→Question 581 Mark
Using square root table, find the square root:
6929
AnswerUsing the table to find $\sqrt{41}$
$\sqrt{6929}=\sqrt{169}\times\sqrt{41}$
$=13\times6.4031$
$=83.239$
View full question & answer→Question 591 Mark
Using square root table, find the square root:
540
AnswerUsing the table to find $\sqrt{3}$ and $\sqrt{5}$
$\sqrt{540}=\sqrt{54}\times\sqrt{10}$
$=2\times3\sqrt{3}\times\sqrt{5}$
$=2\times3\times1.732\times2.2361$
$=23.24$
View full question & answer→Question 601 Mark
Using square root table, find the square root:
3509
AnswerUsing the table to find $\sqrt{29}$
$\sqrt{3509}=\sqrt{121}\times\sqrt{29}$
$=11\times5.3851$
$=59.235$
View full question & answer→Question 611 Mark
Using square root table, find the square root:
198
AnswerUsing the table to find $\sqrt{2}$ and $\sqrt{11}$
$\sqrt{198}=\sqrt{2}\times\sqrt{9}\times\sqrt{11}$
$=1.414\times3\times3.317$
$=14.070$
View full question & answer→Question 621 Mark
Using square root table, find the square root:
15
AnswerUsing the table to find $\sqrt{3}$ and $\sqrt{5}$
$\sqrt{15}=\sqrt{3}\times\sqrt{5}$
$=1.732\times2.236$
$=3.873$
View full question & answer→Question 631 Mark
Using square root table, find the square root:
1110
Answer$\sqrt{1110}=\sqrt{2}\times\sqrt{3}\times\sqrt{5}\times\sqrt{37}$
$=1.414\times1.732\times2.236\times6.083$ (Using the table to find all the square roots)
$=33.312$
View full question & answer→Question 641 Mark
Using square root table, find the square root:
110
Answer$\sqrt{110}=\sqrt{2}\times\sqrt{5}\times\sqrt{11}$
$=1.414\times2.236\times3.317$ (Using the suare root table to find all the square roots)
$=10.488$
View full question & answer→Question 651 Mark
The following numbers are not perfect squares. Give reason.
i. 1547
ii. 45743
iii. 8948
iv. 333333
AnswerA number ending with 2, 3, 7 or 8 cannot be a perfect square.
i. Its last digit is 7. Hence, 1547 cannot be a perfect square.
ii. Its last digit is 3. Hence, 45743 cannot be a perfect square.
iii. Its last digit is 8. Hence, 8948 cannot be a perfect square.
iv. Its last digit is 3. Hence, 333333 cannot be a perfect square.
View full question & answer→Question 661 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{400}{63}$
AnswerFrom the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{400}{63}}=\frac{20}{3\sqrt{7}}$
$=\frac{20}{3\times2.646}=2.520$
View full question & answer→Question 671 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{27}{50}$
AnswerFrom the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{27}{50}}=\frac{3\sqrt{3}}{5\sqrt{2}}=\frac{3\times1.732}{5\times1.414}=0.735$
View full question & answer→Question 681 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{256}{5}$
AnswerFrom the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155$
View full question & answer→Question 691 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{196}{75}$
AnswerFrom the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{196}{75}}=\frac{14}{5\sqrt{3}}$
$=\frac{14}{5\times1.732}=1.617$
View full question & answer→Question 701 Mark
Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{150}{7}$
AnswerFrom the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{150}{7}}=\frac{5\sqrt{2}\times\sqrt{3}}{\sqrt{7}}$
$=\frac{5\times1.414\times1.732}{2.646}=4.628$
View full question & answer→Question 711 Mark
Given that, $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ evaluate each of the following:
$\sqrt{\frac{2500}{3}}$
AnswerGiven,
$\sqrt{3}=1.732$
$\sqrt{\frac{2500}{3}}=\frac{\sqrt{2500}}{\sqrt{3}}=\frac{50}{1.732}=28.867$
View full question & answer→Question 721 Mark
Given that, $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ evaluate each of the following:
$\sqrt{\frac{144}{7}}$
AnswerGiven,
$\sqrt{7}=2.646$
$\sqrt{\frac{144}{7}}=\frac{\sqrt{144}}{\sqrt{7}}=\frac{12}{2.646}=4.536$
View full question & answer→Question 731 Mark
Find the value of:
$\sqrt{72}\times\sqrt{338}$
AnswerWe have,
$\sqrt{72}\times\sqrt{338}=\sqrt{72\times338}$
$=\sqrt{2\times2\times2\times3\times3\times2\times13\times13}$
$=\sqrt{2\times2\times2\times2\times3\times3\times13\times13}$
$=2\times2\times3\times13$
$=156$
View full question & answer→Question 741 Mark
Find the value of:
$\sqrt{45}\times\sqrt{20}$
AnswerWe have,
$\sqrt{45}\times\sqrt{20}=\sqrt{3\times3\times5\times2\times2\times5}$
$=\sqrt{3\times3\times2\times2\times5\times5}$
View full question & answer→Question 751 Mark
Find the value of:
$\frac{\sqrt{80}}{\sqrt{405}}$
AnswerWe have,
$\frac{\sqrt{80}}{\sqrt{405}}=\sqrt{\frac{80}{405}}$
$=\sqrt{\frac{16}{81}}=\frac{\sqrt{16}}{\sqrt{81}}=\frac{4}{9}$
View full question & answer→Question 761 Mark
By just examining the units digits, can you tell which of the following cannot be whole squares?
i. 1026
ii. 1028
iii. 1024
iv. 1022
v. 1023
vi. 1027
AnswerIf the units digit of a number is 2, 3, 7 or 8, the number cannot be a whole square.
i. 1026 has 6 as the units digit, so it is possibly a perfect square.
ii. 1028 has 8 as the units digit, so it cannot be a perfect square.
iii. 1024 has 4 as the units digit, so it is possibly a perfect square.
iv. 1022 has 2 as the units digit, so it cannot be a perfect square.
v. 1023 has 3 as the units digit, so it cannot be a perfect square.
vi. 1027 has 7 as the unit digit, so it cannot be a perfect square.
Hence, by examining the units digits, we can be certain that 1028, 1022, 1023 and 1027 cannot be whole squares.
View full question & answer→