Question

Find the square root of each expression given below:
(i) $3\times 3\times 4\times 4$
(ii) $2\times 2\times 5\times 5$
(iii) $3\times 3\times 3\times 3\times 3\times 3$
(iv) $5\times 5\times 11\times 11\times 7\times 7$

Answer 1

$\left(i\right)3\times 3\times 4\times 4$

$3\times 3\times 4\times 4=3^2\times 4^2=(3\times 4{)}^2$

So square root of $3\times 3\times 4\times 4$ is $3\times 4=12$

(ii) $2\times 2\times 5\times 5$

$2\times 2\times 5\times 5=2^2\times 5^2=(2\times 5{)}^2$

So square root of $2\times 2\times 5\times 5$ is $2\times 5=10$

(iii) $3\times 3\times 3\times 3\times 3\times 3$

$3\times 3\times 3\times 3\times 3\times 3=3^2\times 3^2\times 3^2=(3\times 3\times 3{)}^2$

So square root of $3\times 3\times 3\times 3\times 3\times 3$ is $3\times 3\times 3=27$

$\left(iv\right)5\times 5\times 11\times 11\times 7\times 7$

$5\times 5\times 11\times 11\times 7\times 7=5^2\times {11}^2\times 7^2=(5\times 11\times 7{)}^2$

So square root of $5\times 5\times 11\times 11\times 7\times 7$ is $5\times 11\times 7=385$