Question 12 Marks
Find the square root in decimal from:
0.00002025
0.00002025
Answer
Hence, the square root of 0.00002025 is 0.0045
View full question & answer→Hence, the square root of 0.00002025 is 0.0045Questions · Page 1 of 3
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Question 22 Marks
Find the squares of the following numbers.
512
512
Answer
View full question & answer→$(512)^2$
Here $a=1, b=2$
$\therefore(5 a b)^2=(250+a b) \times 1000+(a b)^2$
$\therefore(512)^2=(250+12) \times 1000+(12)^2$
$=262 \times 1000+144$
$=262000+144$
$=262144$
Here $a=1, b=2$
$\therefore(5 a b)^2=(250+a b) \times 1000+(a b)^2$
$\therefore(512)^2=(250+12) \times 1000+(12)^2$
$=262 \times 1000+144$
$=262000+144$
$=262144$
Question 32 Marks
Using prime factorization method, find the following numbers are perfect squares?
441
441
Answer
View full question & answer→441 = 3 × 3 × 7 × 7
$\begin{array}{c|c} 3& 441 \\ \hline 3 & 147 \\\hline 7&49 \\\hline 7&7\\\hline&1 \end{array}$
Grouping them into pairs of equal factors,
441 = 3 × 3 × (7 × 7)
There are no left out of pairs. Hence, 441 is a perfect square.
$\begin{array}{c|c} 3& 441 \\ \hline 3 & 147 \\\hline 7&49 \\\hline 7&7\\\hline&1 \end{array}$
Grouping them into pairs of equal factors,
441 = 3 × 3 × (7 × 7)
There are no left out of pairs. Hence, 441 is a perfect square.
Question 42 Marks
Find the length of a side of a square playground whose area is equal to the area of a rectangular field of diamensions 72m and 338m.
Answer
View full question & answer→The area of the playground $=72 \times 338=24336 m^2$
The length of one side of a square is equal to the square root of its area. Hence, we just need to find the square root of 24336.
Hence, the length of one side of the playground is 156 metres.
The length of one side of a square is equal to the square root of its area. Hence, we just need to find the square root of 24336.
Hence, the length of one side of the playground is 156 metres.
Question 52 Marks
Find the least number which be added to the following numbers to make tham a perfect square:
4515600
4515600
Answer
View full question & answer→Using the long division method,
We can see that 4515600 is 25 more than $2125^2$. Hence, we have to add 25 to 4515600 to get a perfect square.
We can see that 4515600 is 25 more than $2125^2$. Hence, we have to add 25 to 4515600 to get a perfect square.
Question 62 Marks
The area of a square playground is 256.6404 square metres. Find the length of one side of the playground.
Answer
View full question & answer→The length of one side of the playground is the square root of its area.
So, the length of one side of the playground is 16.02 metres.
So, the length of one side of the playground is 16.02 metres.
Question 72 Marks
The area of a square field is $30\frac{1}{4}\text{m}^2$ Calculate the length of the side of the square.
Answer
View full question & answer→The length of one side is equal to the square root of the area of the field. Hence, we just need to calculate the value of $\sqrt{30\frac{1}{4}}$
Calculate the value of $\sqrt{30\frac{1}{4}}$
We have,
$\sqrt{30\frac{1}{4}}=\frac{\sqrt{121}}{\sqrt{14}}$
Now, calculating the square root of the numerator and the denominator,
$\sqrt{121}=\sqrt{11\times11}=11$
$\sqrt{4}=2$
Therefore, the length of the side of the square $\sqrt{30\frac{1}{4}}=\frac{11}{2}=5\frac{1}{2}\text{m}$
Calculate the value of $\sqrt{30\frac{1}{4}}$
We have,
$\sqrt{30\frac{1}{4}}=\frac{\sqrt{121}}{\sqrt{14}}$
Now, calculating the square root of the numerator and the denominator,
$\sqrt{121}=\sqrt{11\times11}=11$
$\sqrt{4}=2$
Therefore, the length of the side of the square $\sqrt{30\frac{1}{4}}=\frac{11}{2}=5\frac{1}{2}\text{m}$
Question 82 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2$ :
498
498
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(498)^2=(500-5)^2$
$=(500)^2-2 \times 500 \times 2+(2)^2$
$=250000-2000+4$
$=250004-2000$
$=248004$
$(498)^2=(500-5)^2$
$=(500)^2-2 \times 500 \times 2+(2)^2$
$=250000-2000+4$
$=250004-2000$
$=248004$
Question 92 Marks
Find the square root of:
$75\frac{46}{49}$
$75\frac{46}{49}$
Answer
View full question & answer→We know, $\sqrt{75\frac{46}{49}}=\sqrt{\frac{3721}{49}}=\frac{\sqrt{3721}}{\sqrt{49}}$ Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{49}=7$ $\therefore\sqrt{75\frac{46}{49}}=\frac{61}{7}$
$\sqrt{49}=7$ $\therefore\sqrt{75\frac{46}{49}}=\frac{61}{7}$
Question 102 Marks
Find the square root of the following by long division method:4008004
Answer
Hence, the square root of 4008004 is 2002
View full question & answer→Hence, the square root of 4008004 is 2002Question 112 Marks
Find the squares of the following numbers.
$95$
$95$
Answer
View full question & answer→$(95)^2$
$\text { Here } n=9$
$\therefore n(n+1)=9(9+1)$
$=9 \times 10=90$
$\therefore(95)^2=9025$
$\text { Here } n=9$
$\therefore n(n+1)=9(9+1)$
$=9 \times 10=90$
$\therefore(95)^2=9025$
Question 122 Marks
Find the square root of:
$3\frac{942}{2209}$
$3\frac{942}{2209}$
Answer
View full question & answer→We know, $\sqrt{3\frac{942}{2209}}=\sqrt{\frac{7569}{2209}}=\frac{\sqrt{7569}}{\sqrt{2209}}$ Now, let us compute the square roots of the numerator and the denominator separately.
$\therefore\sqrt{3\frac{942}{2209}}=\frac{87}{47}$
$\therefore\sqrt{3\frac{942}{2209}}=\frac{87}{47}$
Question 132 Marks
Find the square root of:
$10\frac{151}{225}$
$10\frac{151}{225}$
Answer
View full question & answer→We know,
$\sqrt{10\frac{151}{225}}=\sqrt{\frac{2401}{225}}=\frac{\sqrt{2401}}{\sqrt{225}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{2401}=\sqrt{7\times7\times7\times7}=7\times7=49$
$\sqrt{225}=\sqrt{3\times3\times5\times5}=3\times5=15$
$\therefore\sqrt{10\frac{151}{225}}=\frac{49}{15}=3\frac{4}{15}$
$\sqrt{10\frac{151}{225}}=\sqrt{\frac{2401}{225}}=\frac{\sqrt{2401}}{\sqrt{225}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{2401}=\sqrt{7\times7\times7\times7}=7\times7=49$
$\sqrt{225}=\sqrt{3\times3\times5\times5}=3\times5=15$
$\therefore\sqrt{10\frac{151}{225}}=\frac{49}{15}=3\frac{4}{15}$
Question 142 Marks
Which of the following triplets are pythagorean?
$(18,80,82)$
$(18,80,82)$
Answer
View full question & answer→A triplet $(a, b, c)$ is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.
The two smallest numbers are 18 and 80 . The sum of their squares is,
$18^2+80^2=6724=82^2$
Hence, $(18,80,82)$ is a Pythagorean triplet.
The two smallest numbers are 18 and 80 . The sum of their squares is,
$18^2+80^2=6724=82^2$
Hence, $(18,80,82)$ is a Pythagorean triplet.
Question 152 Marks
Find the squares of the following numbers using the identity $(a+b)^2=a^2+2 a b+b^2$ :
510
510
Answer
View full question & answer→$(a+b)^2=a^2+2 a b+b^2$
$(510)^2=(500+10)^2$
$=(500)^2+2 \times 500 \times 10 \times(10)^2$
$=250000+10000+100$
$=260100$
$(510)^2=(500+10)^2$
$=(500)^2+2 \times 500 \times 10 \times(10)^2$
$=250000+10000+100$
$=260100$
Question 162 Marks
Find the square root of the following by long division method:82264900
Answer
Hence, the square root of 82264900 is 9070
View full question & answer→Hence, the square root of 82264900 is 9070Question 172 Marks
Find the squares of the following numbers:
$451$
$451$
Answer
View full question & answer→$(451)^2=(400+51)^2$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(400)^2+2 \times 400 \times 51+(51)^2$
$=160000+4080+2601$
$=203401$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(400)^2+2 \times 400 \times 51+(51)^2$
$=160000+4080+2601$
$=203401$
Question 182 Marks
Which of the following triplets are pythagorean?
$(8,15,17)$
$(8,15,17)$
Answer
View full question & answer→A triplet ( $a, b, c$ ) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number. The two smallest numbers are 8 and 15 . The sum of their squares is,
$8^2+15^2=289=17^2$
Hence, $(8,15,17)$ is a Pythagorean triplet.
$8^2+15^2=289=17^2$
Hence, $(8,15,17)$ is a Pythagorean triplet.
Question 192 Marks
Using square root table, find the square root:
25725
25725
Answer
View full question & answer→Using the table to find $\sqrt{3}$ and $\sqrt{7}$$\sqrt{25725}=\sqrt{3\times5\times5\times7\times7\times7}$
$=\sqrt{3}\times5\times7\times\sqrt{7}$
$=1.732\times5\times7\times2.646$
$=160.41$
$=\sqrt{3}\times5\times7\times\sqrt{7}$
$=1.732\times5\times7\times2.646$
$=160.41$
Question 202 Marks
Find the square root of:
$2\frac{137}{196}$
$2\frac{137}{196}$
Answer
View full question & answer→We know,
$\sqrt{2\frac{137}{196}}=\sqrt{\frac{529}{196}}=\frac{\sqrt{529}}{\sqrt{196}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{529}=\sqrt{23\times23}=23$
$\sqrt{196}=\sqrt{2\times2\times7\times7}=2\times7=14$
$\therefore\sqrt{2\frac{137}{196}}=\frac{23}{14}$
$\sqrt{2\frac{137}{196}}=\sqrt{\frac{529}{196}}=\frac{\sqrt{529}}{\sqrt{196}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{529}=\sqrt{23\times23}=23$
$\sqrt{196}=\sqrt{2\times2\times7\times7}=2\times7=14$
$\therefore\sqrt{2\frac{137}{196}}=\frac{23}{14}$
Question 212 Marks
What is that fraction which when multiplied by itself gives 227.798649?
Answer
View full question & answer→We have to find the square root of the given number.
Hence, the fraction, which when multiplied by itself, gives 227.798649 is 15.093
Hence, the fraction, which when multiplied by itself, gives 227.798649 is 15.093
Question 222 Marks
Simplify:
$\frac{\sqrt{59.29}\ -\sqrt{5.29}}{\sqrt{59.29}\ +\sqrt{5.29}}$
$\frac{\sqrt{59.29}\ -\sqrt{5.29}}{\sqrt{59.29}\ +\sqrt{5.29}}$
Answer
View full question & answer→We have,
$\sqrt{59.29}=\sqrt{\frac{5929}{100}}=\frac{\sqrt{7\times7\times11\times11}}{10}=\frac{7\times11}{10}=7.7$
$\sqrt{59.29}=\sqrt{\frac{5929}{100}}=\frac{\sqrt{529}}{\sqrt{100}}=\frac{23}{10}=2.3$
$\frac{\sqrt{59.29}\ -\sqrt{5.29}}{\sqrt{59.29}\ +\sqrt{5.29}}=\frac{7.7-2.3}{7.7+2.3}=\frac{5.4}{10}=0.54$
$\sqrt{59.29}=\sqrt{\frac{5929}{100}}=\frac{\sqrt{7\times7\times11\times11}}{10}=\frac{7\times11}{10}=7.7$
$\sqrt{59.29}=\sqrt{\frac{5929}{100}}=\frac{\sqrt{529}}{\sqrt{100}}=\frac{23}{10}=2.3$
$\frac{\sqrt{59.29}\ -\sqrt{5.29}}{\sqrt{59.29}\ +\sqrt{5.29}}=\frac{7.7-2.3}{7.7+2.3}=\frac{5.4}{10}=0.54$
Question 232 Marks
Find the value of:
$\frac{\sqrt{1587}}{\sqrt{1728}}$
$\frac{\sqrt{1587}}{\sqrt{1728}}$
Answer
View full question & answer→We have,
$\frac{\sqrt{1587}}{\sqrt{1728}}=\sqrt{\frac{529}{576}}$ (by dividing both numbers by 3)
Computing the square roots of the numerator and the denominator,
$\sqrt{529}=\sqrt{23\times23}=23$
$\sqrt{576}=\sqrt{24\times24}=24$
$\therefore\frac{\sqrt{1587}}{\sqrt{1728}}=\frac{23}{24}$
$\frac{\sqrt{1587}}{\sqrt{1728}}=\sqrt{\frac{529}{576}}$ (by dividing both numbers by 3)
Computing the square roots of the numerator and the denominator,
$\sqrt{529}=\sqrt{23\times23}=23$
$\sqrt{576}=\sqrt{24\times24}=24$
$\therefore\frac{\sqrt{1587}}{\sqrt{1728}}=\frac{23}{24}$
Question 242 Marks
Find the square root of the following by long division method:62504836
Answer
Hence, the square root of 6250486 is 7906
View full question & answer→Hence, the square root of 6250486 is 7906Question 252 Marks
Find the square root in decimal from:
0.813604
0.813604
Answer
Hence, the square root of 0.813604 is 0.902
View full question & answer→Hence, the square root of 0.813604 is 0.902
Question 262 Marks
Find the least number which be added to the following numbers to make tham a perfect square:
$506900$
$506900$
Answer
View full question & answer→Using the long division method
,
We can see that 506900 is 44 more than $712^2$. Hence, we have to add 44 to 506900 to get a perfect square.
,
We can see that 506900 is 44 more than $712^2$. Hence, we have to add 44 to 506900 to get a perfect square.
Question 272 Marks
Find the least number which be added to the following numbers to make tham a perfect square:
5607
5607
Answer
View full question & answer→Using the long division method,
We can see that 5607 is 18 more than $75^2$. Hence, we have to add 18 to 5607 to get a perfect square.
We can see that 5607 is 18 more than $75^2$. Hence, we have to add 18 to 5607 to get a perfect square.
Question 282 Marks
Find the least number which must be subtracted from the following numbers to make tham a perfact square:
26535
26535
Answer
View full question & answer→Using the long division method,
We can see that 26535 is 291 more than $162^2$. Hence, 291 must be subtracted from 26535 to get a perfect square.
We can see that 26535 is 291 more than $162^2$. Hence, 291 must be subtracted from 26535 to get a perfect square.
Question 292 Marks
Find the squares of the following numbers using the identity $(a+b)^2=a^2+2 a b+b^2$ :
209
209
Answer
View full question & answer→$(a+b)^2=a^2+2 a b+b^2$
$(209)^2=(200+9)^2$
$=(200)^2+2 \times 200 \times 9 \times(9)^2$
$=40000+3600+81$
$=43681$
$(209)^2=(200+9)^2$
$=(200)^2+2 \times 200 \times 9 \times(9)^2$
$=40000+3600+81$
$=43681$
Question 302 Marks
Using square root table, find the square root,
11.11
11.11
Answer
View full question & answer→We have,
$\sqrt{11}=3.317$ and $\sqrt{12}=3.464$
Their difference is 0.1474
Thus, for the difference of 1 (12 - 11), the difference in the value of the square roots is 0.1474
For the difference of 0.11, the difference in the values of the square roots is,
0.11 × 0.1474 = 0.0162
$\therefore\sqrt{11.11}=3.3166+0.0162=3.328\approx3.333$
$\sqrt{11}=3.317$ and $\sqrt{12}=3.464$
Their difference is 0.1474
Thus, for the difference of 1 (12 - 11), the difference in the value of the square roots is 0.1474
For the difference of 0.11, the difference in the values of the square roots is,
0.11 × 0.1474 = 0.0162
$\therefore\sqrt{11.11}=3.3166+0.0162=3.328\approx3.333$
Question 312 Marks
Write the possible unit's digits of the square root of the following numbers. these numbers are odd square roots?
$9801$
$9801$
Answer
View full question & answer→The unit digit of the number 9801 is 1 . So, the possible unit digits are 1 or 9 (Table 3.4 ). Note that 9801 is equal to $99^2$. Hence, the square root is an odd number.
Question 322 Marks
Find the square root of the following by long division method:
1745041
1745041
Answer
Hence, the square root of 1745041 is 1321
View full question & answer→Hence, the square root of 1745041 is 1321Question 332 Marks
Using prime factorization method, find the following numbers are perfect squares?
3549
3549
Answer
View full question & answer→3549 = 3 × 7 × 13 × 13
$\begin{array}{c|c} 3& 3549 \\ \hline 7 & 1183 \\\hline 13&169 \\\hline 13&13 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
3549 = (13 × 13) × 3 × 7
The last factors, 3 and 7 cannot be paired. Hence, 3549 is not a perfect square.
Hence, the perfect squares are 225, 441, 2916 and 11025.
$\begin{array}{c|c} 3& 3549 \\ \hline 7 & 1183 \\\hline 13&169 \\\hline 13&13 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
3549 = (13 × 13) × 3 × 7
The last factors, 3 and 7 cannot be paired. Hence, 3549 is not a perfect square.
Hence, the perfect squares are 225, 441, 2916 and 11025.
Question 342 Marks
Find the square root in decimal from:225.6004
Answer
Hence, the square root of 225.6004 is 15.25
View full question & answer→Hence, the square root of 225.6004 is 15.25Question 352 Marks
Find the square root of the following by long division method:
12544
12544
Answer
Hence, the square root of 12544 is 112
View full question & answer→Hence, the square root of 12544 is 112
Question 362 Marks
Find the squares of the following numbers.
$425$
$425$
Answer
View full question & answer→$(425)^2$
Here $n =42$
$\therefore n(n+1)=42(42+1)$
$=42 \times 43=1806$
$\therefore(425)^2=180625$
Here $n =42$
$\therefore n(n+1)=42(42+1)$
$=42 \times 43=1806$
$\therefore(425)^2=180625$
Question 372 Marks
Find the square root in decimal form:9998.0001
Answer
Hence, the square root of 9998.001 is 99.99
View full question & answer→Hence, the square root of 9998.001 is 99.99Question 382 Marks
Observe the following pattern,
$1+3=2^2$
$1+3+5=3^2$
$1+3+5+7=4^2$
and write the value of $1+3+5+7+9+$ ...... upto n terms.
$1+3+5=3^2$
$1+3+5+7=4^2$
and write the value of $1+3+5+7+9+$ ...... upto n terms.
Answer
View full question & answer→From the pattern, we can say that the sum of the first $n$ positive odd numbers is equal to the square of the $n ^{\text {th }}$ positive number. Putting that into for $1+3+5+7+\ldots \ldots . n=n^2$, where the left hand side consists of $n$ terms.
Question 392 Marks
Find the square root in decimal form:
236.144689
236.144689
Answer
Hence, the square root of 236.144689 is 15.367
View full question & answer→Hence, the square root of 236.144689 is 15.367
Question 402 Marks
Find the square root of the following by long division method:152547201
Answer
Hence, the square root of 152547201 is 12351
View full question & answer→Hence, the square root of 152547201 is 12351Question 412 Marks
Find the least number which must be subtracted from the following numbers to make tham a perfact square:
$16160$
$16160$
Answer
View full question & answer→Using the long division method,
We can see that 16160 is 31 more than $127^2$. Hence, 31 must be subtracted from 16160 to get a perfect square.
We can see that 16160 is 31 more than $127^2$. Hence, 31 must be subtracted from 16160 to get a perfect square.
Question 422 Marks
Find the square root of the following by long division method:3915380329
Answer
Hence, the square root of 3915380329 is 625763
View full question & answer→Hence, the square root of 3915380329 is 625763Question 432 Marks
Find the squares of the following numbers.
205
205
Answer
View full question & answer→$(205)^2$
Here $n =20$
$\therefore n(n+1)=20(20+1)$
$=20 \times 21=420$
$\therefore(205)^2=42025$
Here $n =20$
$\therefore n(n+1)=20(20+1)$
$=20 \times 21=420$
$\therefore(205)^2=42025$
Question 442 Marks
Find the square root in decimal form:0.00038809
Answer
Hence, the square root of 0.00038809 is 0.0197
View full question & answer→Hence, the square root of 0.00038809 is 0.0197
Question 452 Marks
Which of the following triplets are pythagorean?
$(10,24,26)$
$(10,24,26)$
Answer
View full question & answer→A triplet ( $a, b, c$ ) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number. The two smallest numbers are 10 and 24 . The sum of their squares is,
$10^2+24^2=676=26^2$
Hence, $(10,24,26)$ is a Pythagorean triplet.
$10^2+24^2=676=26^2$
Hence, $(10,24,26)$ is a Pythagorean triplet.
Question 462 Marks
Find the value of $\sqrt{103.0225}$ and hence find the value of:
$\sqrt{1.030225}$
$\sqrt{1.030225}$
Answer
View full question & answer→The value of 103.0225 is,
Hence, the square root of 103.0225 is 10.15
$\sqrt{1.030225}=\sqrt{\frac{103.0225}{100}}$
$=\frac{\sqrt{103.0225}}{\sqrt{100}}=\frac{{10.15}}{10}=1.015$
Hence, the square root of 103.0225 is 10.15
$\sqrt{1.030225}=\sqrt{\frac{103.0225}{100}}$
$=\frac{\sqrt{103.0225}}{\sqrt{100}}=\frac{{10.15}}{10}=1.015$
Question 472 Marks
Find the square root of the following by long division method:
120409
120409
Answer
Hence, the square root of 120409 is 347
View full question & answer→Hence, the square root of 120409 is 347Question 482 Marks
Using square root table, find the square root:
1312
1312
Answer
View full question & answer→Using the table to find $\sqrt{2}$ and $\sqrt{41}$$\sqrt{1312}=\sqrt{2\times2\times2\times2\times2\times41}$
$=2\times2\sqrt{2}\times\sqrt{41}$
$=2\times2\times1.414\times6.4031$
$=36.222$
$=2\times2\sqrt{2}\times\sqrt{41}$
$=2\times2\times1.414\times6.4031$
$=36.222$
Question 492 Marks
Using prime factorization method, find the following numbers are perfect squares?
343
343
Answer
View full question & answer→343 = 7 × 7 × 7
$\begin{array}{c|c} 7& 343 \\ \hline 7 & 49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
343 = (7 × 7) × 7
The last factor, 7 cannot be paired. Hence, 343 is not a perfect square.
$\begin{array}{c|c} 7& 343 \\ \hline 7 & 49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
343 = (7 × 7) × 7
The last factor, 7 cannot be paired. Hence, 343 is not a perfect square.
Question 502 Marks
Find the square root of the following by long division method:
974169
974169
Answer
Hence, the square root of 974169 is 987
View full question & answer→Hence, the square root of 974169 is 987