Question

Find the square root of the following:
(i) $\frac{225}{3136}$

(ii) $\frac{2116}{3481}$

(iii) $\frac{529}{1764}$

(iv) $\frac{7921}{5776}$

Answer 1

(i) $225/3136$

$225/3136=(3\times 3\times 5\times 5)/(2\times 2\times 2\times 2\times 2\times 2\times 7\times 7)=(3^2\times 5^2)/(2^2\times 2^2\times 2^2\times 7^2)$

$=\left(\right(3\times 5\left)/\right(2\times 2\times 2\times 7){)}^2$

So square root of $225/3136$ is $(3\times 5)/(2\times 2\times 2\times 7)=15/56$

(ii) $2116/3481$

$2116/3481=(2\times 2\times 23\times 23)/(59\times 59)=(2^2\times {23}^2)/\left({59}^2\right)=\left(\right(2\times 23\left)/{59}^2\right)$

So square root of $2116/3418$ is $(2\times 23)/\left(59\right)=46/59$

(iii) $529/1764$

$529/1764=(23\times 23)/(2\times 2\times 3\times 3\times 7\times 7)=\left({23}^2\right)/(2^2\times 3^2\times 7^2)=\left(23/\right(2\times 3\times 7){)}^2$

So square root of $529/1764$ is $\left(23\right)/(2\times 3\times 7)=23/42$

(iv) $7921/5776$

$7921/5776=(89\times 89)/(2\times 2\times 2\times 2\times 19\times 19)=\left({89}^2\right)/(2^2\times 2^2\times {19}^2)=\left(89/\right(2\times 2\times 19){)}^2$

So square root of $7921/5776$ is $\left(89\right)/(2\times 2\times 19)=89/76$