Question

Find the square root of the following:
(i) $\frac{9}{64}$
(ii) $\frac{1}{16}$
(iii) $49$
(iv) $16$

Answer 1

$\left(i\right)9/64$

$9/64=(3\times 3)/(2\times 2\times 2\times 2\times 2\times 2)=3^2/(2^2\times 2^2\times 2^2)=\left(3/\right(2\times 2\times 2){)}^2$

So square root of $9/64$ is $3/(2\times 2\times 2)=3/8$

$\left(ii\right)1/16$

$1/16=1/(2\times 2\times 2\times 2)=1/(2^2\times 2^2)=(1/4{)}^2$

So square root of $1/16$ is $1/4$

$\left(iii\right)49$

$49=7\times 7=7^2$

So square root of $49$ is $7$

$\left(iv\right)16$

$16=2\times 2\times 2\times 2=2^2\times 2^2=(2\times 2{)}^2$

So square root of 16 is $2\times 2=4$