Question 512 Marks
Find the square root of the following by long division method:
1471369
1471369
Answer
Hence, the square root of 1471369 is 1213
View full question & answer→Hence, the square root of 1471369 is 1213Questions · Page 2 of 3
2 Mark Question
Question 522 Marks
Find the square root of:
$\frac{324}{841}$
$\frac{324}{841}$
Answer
View full question & answer→We know,
$\sqrt{\frac{324}{841}}=\frac{\sqrt{324}}{\sqrt{841}}$
Now, let compute the square roots of the numberator and the denominator separately.
$\sqrt{324}=\sqrt{2\times2\times3\times3\times3\times3}$
$\sqrt{841}=\sqrt{29\times29}=29$
$\therefore\sqrt{\frac{324}{841}}=\frac{81}{29}$
$\sqrt{\frac{324}{841}}=\frac{\sqrt{324}}{\sqrt{841}}$
Now, let compute the square roots of the numberator and the denominator separately.
$\sqrt{324}=\sqrt{2\times2\times3\times3\times3\times3}$
$\sqrt{841}=\sqrt{29\times29}=29$
$\therefore\sqrt{\frac{324}{841}}=\frac{81}{29}$
Question 532 Marks
Find the square root of the following by long division method:
9653449
9653449
Answer
Hence, the square root of 9653449 is 3107
View full question & answer→Hence, the square root of 9653449 is 3107Question 542 Marks
Find the squares of the following numbers using the identity $(a+b)^2=a^2+2 a b+b^2$ :
405
405
Answer
View full question & answer→$(a+b)^2=a^2+2 a b+b^2$
$(405)^2=(400+5)^2$
$=(400)^2+2 \times 400 \times 5+(5)^2$
$=160000+4000+25$
$=164025$
$(405)^2=(400+5)^2$
$=(400)^2+2 \times 400 \times 5+(5)^2$
$=160000+4000+25$
$=164025$
Question 552 Marks
Find the squares of the following numbers.
$575$
$575$
Answer
View full question & answer→$(575)^2$
$\text { Here } n=57$
$\therefore n(n+1)=57(57+1)$
$=57 \times 58=3306$
$\therefore(575)^2=330625$
$\text { Here } n=57$
$\therefore n(n+1)=57(57+1)$
$=57 \times 58=3306$
$\therefore(575)^2=330625$
Question 562 Marks
Find the square root of:
$2\frac{14}{25}$
$2\frac{14}{25}$
Answer
View full question & answer→We know,
$\sqrt{2\frac{14}{25}}=\sqrt{\frac{64}{65}}=\frac{\sqrt{64}}{\sqrt{25}}=\frac{8}{5}$
$\sqrt{2\frac{14}{25}}=\sqrt{\frac{64}{65}}=\frac{\sqrt{64}}{\sqrt{25}}=\frac{8}{5}$
Question 572 Marks
Find the value of:
$\frac{\sqrt{441}}{\sqrt{625}}$
$\frac{\sqrt{441}}{\sqrt{625}}$
Answer
View full question & answer→Computing the square roots,
$\sqrt{441}=\sqrt{(3\times3)\times(7\times7)}=3\times7=21$
$\sqrt{625}=\sqrt{(5\times5)\times(5\times5)=5\times5}=25$
$\therefore\frac{\sqrt{441}}{\sqrt{625}}=\frac{21}{25}$
$\sqrt{441}=\sqrt{(3\times3)\times(7\times7)}=3\times7=21$
$\sqrt{625}=\sqrt{(5\times5)\times(5\times5)=5\times5}=25$
$\therefore\frac{\sqrt{441}}{\sqrt{625}}=\frac{21}{25}$
Question 582 Marks
Find the square root of:
$21\frac{2797}{3364}$
$21\frac{2797}{3364}$
Answer
View full question & answer→We know, $\sqrt{21\frac{2797}{3364}}=\sqrt{\frac{73441}{3364}}=\frac{\sqrt{73441}}{\sqrt{3364}}$ Now, let us compute the square roots of the numerator and the denominator separately.
$\therefore\sqrt{21\frac{2797}{3364}}=\frac{271}{58}$
$\therefore\sqrt{21\frac{2797}{3364}}=\frac{271}{58}$
Question 592 Marks
Find the squares of the following numbers.
$405$
$405$
Answer
View full question & answer→$(405)^2$
$\text { Here } n=40$
$\therefore n(n+1)=40(40+1)$
$=40 \times 41=1640$
$\therefore(405)^2=164025$
$\text { Here } n=40$
$\therefore n(n+1)=40(40+1)$
$=40 \times 41=1640$
$\therefore(405)^2=164025$
Question 602 Marks
Find the square root of:
$25\frac{544}{729}$
$25\frac{544}{729}$
Answer
View full question & answer→We know, $\sqrt{25\frac{544}{729}}=\sqrt{\frac{18769}{729}}=\frac{\sqrt{18769}}{\sqrt{729}}$ Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{729}=27$ $\therefore\sqrt{25\frac{544}{729}}=\frac{137}{27}$
$\sqrt{729}=27$ $\therefore\sqrt{25\frac{544}{729}}=\frac{137}{27}$
Question 612 Marks
Find the square root in decimal from:
0.7225
0.7225
Answer
Hence, the square root of 0.7225 is 0.85
View full question & answer→Hence, the square root of 0.7225 is 0.85Question 622 Marks
Find the square root of the following by long division method:
363609
363609
Answer
Hence, the square root of 363609 is 603
View full question & answer→Hence, the square root of 363609 is 603Question 632 Marks
Find the smallest number which must be added to 2300 so that it becomes a perfect square.
Answer
View full question & answer→To find the square root of 2300, we use the long division method,
23000 is $4(704-700)$ less than $48^2$. Hence, 4 must be added to 2300 to get a perfect square.
23000 is $4(704-700)$ less than $48^2$. Hence, 4 must be added to 2300 to get a perfect square.
Question 642 Marks
Which of the following triplets are pythagorean?
$(14,48,51)$
$(14,48,51)$
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.
He two smallest numbers are 14 and 48 .The sum of their squares is,
$14^2+48^2=2500$, which is not equal to $51^2=2601$
Hence, $(14,48,51)$ is not a Pythagorean triplet.
He two smallest numbers are 14 and 48 .The sum of their squares is,
$14^2+48^2=2500$, which is not equal to $51^2=2601$
Hence, $(14,48,51)$ is not a Pythagorean triplet.
Question 652 Marks
Which of the following triplets are pythagorean?
$(16,63,65)$
$(16,63,65)$
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 16 and 63 . The sum of their squares is,
$16^2+63^2=4225=65^2$
Hence, $(16,63,65)$ is a Pythagorean triplet.
$16^2+63^2=4225=65^2$
Hence, $(16,63,65)$ is a Pythagorean triplet.
Question 662 Marks
Find the squares of the following numbers using the identity $(a+b)^2=a^2+2 a b+b^2$ :
$605$
$605$
Answer
View full question & answer→$(a+b)^2=a^2+2 a b+b^2 \\
(605)^2=(600+5)^2 \\
=(600)^2+2 \times 600 \times 5 \times(5)^2 \\
=360000+6000+25 \\
=366025$
(605)^2=(600+5)^2 \\
=(600)^2+2 \times 600 \times 5 \times(5)^2 \\
=360000+6000+25 \\
=366025$
Question 672 Marks
Find the square root of:
$23\frac{394}{729}$
$23\frac{394}{729}$
Answer
View full question & answer→We know,
$\sqrt{23\frac{394}{729}}=\sqrt{\frac{17161}{729}}=\frac{\sqrt{17161}}{\sqrt{729}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{729}=27$
$\therefore\sqrt{23\frac{394}{729}}=\frac{131}{27}=4\frac{23}{27}$
$\sqrt{23\frac{394}{729}}=\sqrt{\frac{17161}{729}}=\frac{\sqrt{17161}}{\sqrt{729}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{729}=27$
$\therefore\sqrt{23\frac{394}{729}}=\frac{131}{27}=4\frac{23}{27}$
Question 682 Marks
The area of a square field is $325m^2$. Find the approximate length of one side of the field.
Answer
View full question & answer→The length of one side of the square field will be the square root of 325
$\therefore\sqrt{325}=\sqrt{5\times5\times13}$
$=5\times\sqrt{13}$
$=5\times3.605$
$=18.030$
Hence, the length of one side of the field is 18.030m
$\therefore\sqrt{325}=\sqrt{5\times5\times13}$
$=5\times\sqrt{13}$
$=5\times3.605$
$=18.030$
Hence, the length of one side of the field is 18.030m
Question 692 Marks
Find the square root in decimal form:176.252176
Answer
Hence, the square root of 0.00059049 is 0.0243
View full question & answer→Hence, the square root of 0.00059049 is 0.0243Question 702 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2$ :
$995$
$995$
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(995)^2=(1000-5)^2$
$=(1000)^2-2 \times 1000 \times 5+(5)^2$
$=1000000-10000+25$
$=1000025-10000$
$=990025$
$(995)^2=(1000-5)^2$
$=(1000)^2-2 \times 1000 \times 5+(5)^2$
$=1000000-10000+25$
$=1000025-10000$
$=990025$
Question 712 Marks
Find the squares of the following numbers.
$995$
$995$
Answer
View full question & answer→$(995)^2$
$\text { Here } n=99$
$\therefore n(n+1)=99(99+1)$
$=99 \times 100$
$=9900$
$\therefore(995)^2=990025$
$\text { Here } n=99$
$\therefore n(n+1)=99(99+1)$
$=99 \times 100$
$=9900$
$\therefore(995)^2=990025$
Question 722 Marks
Find the square root of:
$\frac{441}{961}$
$\frac{441}{961}$
Answer
View full question & answer→We know,
$\sqrt{\frac{441}{961}}=\frac{\sqrt{441}}{\sqrt{961}}$
Now, let compute the square roots of the numberator and the denominator separately.
$\sqrt{441}=\sqrt{(3\times3)\times(7\times7)}=3\times7=21$
$\sqrt{961}=\sqrt{31\times31}=31$
$\therefore\sqrt{\frac{441}{961}}=\frac{21}{31}$
$\sqrt{\frac{441}{961}}=\frac{\sqrt{441}}{\sqrt{961}}$
Now, let compute the square roots of the numberator and the denominator separately.
$\sqrt{441}=\sqrt{(3\times3)\times(7\times7)}=3\times7=21$
$\sqrt{961}=\sqrt{31\times31}=31$
$\therefore\sqrt{\frac{441}{961}}=\frac{21}{31}$
Question 732 Marks
Find the least number which be added to the following numbers to make tham a perfect square:
4931
4931
Answer
View full question & answer→Using the long division method,
We can see that 4931 is 110 more than $71^2$. Hence, we have to add 110 to 4931 to get a perfect square.
We can see that 4931 is 110 more than $71^2$. Hence, we have to add 110 to 4931 to get a perfect square.
Question 742 Marks
Using prime factorization method, find the following numbers are perfect squares?
225
225
Answer
View full question & answer→225 = 3 × 3 × 5 × 5
$\begin{array}{c|c} 3& 225 \\ \hline 3 & 75 \\\hline 5&25 \\\hline 5&5 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
225 = (3 × 3) × (5 × 5)
There are no left out of pairs. Hence, 225 is a perfect square.
$\begin{array}{c|c} 3& 225 \\ \hline 3 & 75 \\\hline 5&25 \\\hline 5&5 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
225 = (3 × 3) × (5 × 5)
There are no left out of pairs. Hence, 225 is a perfect square.
Question 752 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2$ :
99
99
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(99)^2=(100-1)^2$
$=(100)^2-2 \times 100 \times 1+(1)^2$
$=10000-200+1$
$=10001-200$
$=9801$
$(99)^2=(100-1)^2$
$=(100)^2-2 \times 100 \times 1+(1)^2$
$=10000-200+1$
$=10001-200$
$=9801$
Question 762 Marks
Find the value of $\sqrt{103.0225}$ and hence find the value of:
$\sqrt{10302.25}$
$\sqrt{10302.25}$
Answer
View full question & answer→The value of 103.0225 is,
Hence, the square root of 103.0225 is 10.15
$\sqrt{10302.25}=\sqrt{103.0225\times100}$
$=\sqrt{103.0225}\times{100}=10.15\times10=101.5$
Hence, the square root of 103.0225 is 10.15
$\sqrt{10302.25}=\sqrt{103.0225\times100}$
$=\sqrt{103.0225}\times{100}=10.15\times10=101.5$
Question 772 Marks
Find the square root of:
$21\frac{51}{169}$
$21\frac{51}{169}$
Answer
View full question & answer→We know,
$\sqrt{21\frac{51}{169}}=\sqrt{\frac{3600}{169}}=\frac{\sqrt{3600}}{\sqrt{169}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{3600}=\sqrt{60\times60}=60$
$\sqrt{169}=\sqrt{13\times13}=13$
$\therefore\sqrt{21\frac{51}{169}}=\frac{60}{13}=4\frac{8}{13}$
$\sqrt{21\frac{51}{169}}=\sqrt{\frac{3600}{169}}=\frac{\sqrt{3600}}{\sqrt{169}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{3600}=\sqrt{60\times60}=60$
$\sqrt{169}=\sqrt{13\times13}=13$
$\therefore\sqrt{21\frac{51}{169}}=\frac{60}{13}=4\frac{8}{13}$
Question 782 Marks
Find the square root of the following by long division method:6407522209
Answer
Hence, the square root of 6407522209 is 80047
View full question & answer→Hence, the square root of 6407522209 is 80047Question 792 Marks
Find the least number of three digits which is perfect square.
Answer
View full question & answer→Let us make a list of the squares starting from 1.
$1^2=1$
$2^2=4$
$3^2=9$
$4^2=16$
$5^2=25$
$6^2=36$
$7^2=49$
$8^2=64$
$9^2=81$
$10^2=100$
The square of 10 has three digits. Hence, the least three-digit perfect square is 100
$1^2=1$
$2^2=4$
$3^2=9$
$4^2=16$
$5^2=25$
$6^2=36$
$7^2=49$
$8^2=64$
$9^2=81$
$10^2=100$
The square of 10 has three digits. Hence, the least three-digit perfect square is 100
Question 802 Marks
Using prime factorization method, find the following numbers are perfect squares?
11025
11025
Answer
View full question & answer→11025 = 3 × 3 × 5 × 5 × 7 × 7
$\begin{array}{c|c} 3& 11025 \\ \hline 3 & 3675 \\\hline 5&1225 \\\hline 5&245 \\\hline 7&49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
11025 = (3 × 2) × (5 × 5) × (7 × 7)
There are no left out of pairs. Hence, 11025 is a perfect square.
$\begin{array}{c|c} 3& 11025 \\ \hline 3 & 3675 \\\hline 5&1225 \\\hline 5&245 \\\hline 7&49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
11025 = (3 × 2) × (5 × 5) × (7 × 7)
There are no left out of pairs. Hence, 11025 is a perfect square.
Question 812 Marks
Find the least number which be added to the following numbers to make tham a perfect square:
37460
37460
Answer
View full question & answer→Using the long division method,
We can see that 194491 is 10 more than $441^2$. Hence, 10 must be subtracted from 194491 to get a perfact square.
We can see that 194491 is 10 more than $441^2$. Hence, 10 must be subtracted from 194491 to get a perfact square.
Question 822 Marks
What is the fraction which when multiplied by itself gives 0.00053361?
Answer
View full question & answer→We have to find the square root of the given number.
Hence, the fraction which multiplied by itself, gives 0.00053361 is 0.0231
Hence, the fraction which multiplied by itself, gives 0.00053361 is 0.0231
Question 832 Marks
Find the squares of the following numbers:
$127$
$127$
Answer
View full question & answer→$(127)^2=(120+7)^2$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(120)^2+2 \times 120 \times 7+(7)^2$
$=14400+1680+49$
$=16129$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(120)^2+2 \times 120 \times 7+(7)^2$
$=14400+1680+49$
$=16129$
Question 842 Marks
Find the least number which must be subtracted from the following numbers to make tham a perfact square:
$2361$
$2361$
Answer
View full question & answer→Using the long division method,
We can see that 2361 is 57 more than $47^2$. Hence, 57 must be subtracted from 2361 to get perfact square.
We can see that 2361 is 57 more than $47^2$. Hence, 57 must be subtracted from 2361 to get perfact square.
Question 852 Marks
Find the square root of the following by long division method:20421361
Answer
Hence, the square root of 20421361 is 4519
View full question & answer→Hence, the square root of 20421361 is 4519Question 862 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2$ :
$395$
$395$
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(395)^2=(400-5)^2$
$=(400)^2-2 \times 400 \times 5+(5)^2$
$=160000-4000+25$
$=160025-4000$
$=156025$
$(395)^2=(400-5)^2$
$=(400)^2-2 \times 400 \times 5+(5)^2$
$=160000-4000+25$
$=160025-4000$
$=156025$
Question 872 Marks
Find the square root of the following by long division method:20657025
Answer
Hence, the square root of 20657025 is 4545
View full question & answer→Hence, the square root of 20657025 is 4545Question 882 Marks
Find the square root of the following by long division method:
390625
390625
Answer
Hence, the square root of 390625 is 625
View full question & answer→Hence, the square root of 390625 is 625Question 892 Marks
Find the squares of the following numbers:
$265$
$265$
Answer
View full question & answer→$(265)^2=(200+65)^2$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(200)^2+2 \times 200 \times 65+(65)^2$
$=40000+26000+4225$
$=70225$
$\left\{(a+b)^2=a^2+2 a b+b^2\right\}$
$=(200)^2+2 \times 200 \times 65+(65)^2$
$=40000+26000+4225$
$=70225$
Question 902 Marks
Find the square root in decimal from:
84.8241
84.8241
Answer
Hence, the square root of 84.8241 is 9.21
View full question & answer→Hence, the square root of 84.8241 is 9.21
Question 912 Marks
Find the square root in decimal from:150.0625
Answer
Hence, the square root of 150.0625 is 12.25
View full question & answer→Hence, the square root of 150.0625 is 12.25Question 922 Marks
Find the square root of:
$23\frac{26}{121}$
$23\frac{26}{121}$
Answer
View full question & answer→We know,
$\sqrt{23\frac{26}{121}}=\sqrt{\frac{2809}{121}}=\frac{\sqrt{2809}}{\sqrt{121}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{121}=11$
$\therefore\sqrt{23\frac{26}{121}}=\frac{53}{11}$
$\sqrt{23\frac{26}{121}}=\sqrt{\frac{2809}{121}}=\frac{\sqrt{2809}}{\sqrt{121}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{121}=11$
$\therefore\sqrt{23\frac{26}{121}}=\frac{53}{11}$
Question 932 Marks
Find the square root of the following by long division method:
286225
286225
Answer
Hence, the square root of 286225 is 535
View full question & answer→Hence, the square root of 286225 is 535Question 942 Marks
Find the greatest number of two digits which is a perfect square.
Answer
View full question & answer→We know that $10^2$ is equal to 100 and $9^2$ is equal to 81 . Since 10 and 9 are consecutive numbers, there is no perfect square between 100 and 81 . Since 100 is the first perfect square that has more than two digits, 81 is the greatest two-digit perfect square.
Question 952 Marks
Find the square root of the following by long division method:
97344
97344
Answer
Hence, the square root of 97344 is 312
View full question & answer→Hence, the square root of 97344 is 312Question 962 Marks
Write the possible unit's digits of the square root of the following numbers. these numbers are odd square roots?
657666025
657666025
Answer
View full question & answer→The unit digit of the number 657666025 is 5 . So, the only possible unit digit is 5 . Note that 657666025 is equal to $(5 \times 23 \times 223)^2$. Hence, the square root is an odd number.
Question 972 Marks
Find the square root of:
$4\frac{29}{49}$
$4\frac{29}{49}$
Answer
View full question & answer→We know,
$\sqrt{4\frac{29}{49}}=\sqrt{\frac{225}{49}}=\frac{\sqrt{225}}{\sqrt{49}}$
$\sqrt{225}=15$
$\sqrt{49}=7$
$\therefore\sqrt{4\frac{29}{49}}=\frac{15}{7}$
$\sqrt{4\frac{29}{49}}=\sqrt{\frac{225}{49}}=\frac{\sqrt{225}}{\sqrt{49}}$
$\sqrt{225}=15$
$\sqrt{49}=7$
$\therefore\sqrt{4\frac{29}{49}}=\frac{15}{7}$
Question 982 Marks
Write the possible unit's digits of the square root of the following numbers. these numbers are odd square roots?
99856
99856
Answer
View full question & answer→The unit digit of the number 99856 is 6. So, the possible unit digits are 4 or 6 (Table 3.4). Since its last digit is 6 (an even number), it cannot have an odd number as its square root.
Question 992 Marks
Find the square root of:
$3\frac{334}{3025}$
$3\frac{334}{3025}$
Answer
View full question & answer→We know,
$\sqrt{3\frac{334}{3025}}=\sqrt{\frac{9409}{3025}}=\frac{\sqrt{9409}}{\sqrt{3025}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\therefore\sqrt{3\frac{334}{3035}}=\frac{97}{55}$
$\sqrt{3\frac{334}{3025}}=\sqrt{\frac{9409}{3025}}=\frac{\sqrt{9409}}{\sqrt{3025}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\therefore\sqrt{3\frac{334}{3035}}=\frac{97}{55}$
Question 1002 Marks
Find the squares of the following numbers using the identity $(a-b)^2=a^2-2 a b+b^2$ :
$495$
$495$
Answer
View full question & answer→$(a-b)^2=a^2-2 a b+b^2$
$(495)^2=(500-5)^2$
$=(500)^2-2 \times 500 \times 5+(5)^2$
$=250000-5000+25$
$=250025-5000$
$=245025$
$(495)^2=(500-5)^2$
$=(500)^2-2 \times 500 \times 5+(5)^2$
$=250000-5000+25$
$=250025-5000$
$=245025$