Question

Find the square root of $1089$ using prime factorization.

Answer 1

Finding the square root using prime factorization

Given number $1089$

A perfect square can always be expressed as a product of pairs of equal factors.

So, $1089=3\times 3\times 11\times 11=3^2\times {11}^2$

Hence, square root of $1089=\sqrt{3^2\times {11}^2}=3\times 11=33$ .