Question

Find the square root of a given number by the prime factorization method.

$900$

Answer 1

We will write $900$ as product of its prime factors,

$900=2\times 2\times 3\times 3\times 5\times 5$

$=2^2\times 3^2\times 5^2$

$=(2\times 3\times 5{)}^2$

$={30}^2$

$\Rightarrow \sqrt{900}=30$