Question

Find the square root of $5625$ by prime factorization method.

Answer 1

Step 1: Find the prime factors

The prime factors of $5625$ are

$5625=5\times 5\times 5\times 5\times 3\times 3$

Step 2: Find the square root

The square root of $5625$ is

$$\begin{gathered} 5625=5\times 5\times 5\times 5\times 3\times 3 \\ \Rightarrow \sqrt{5625}=\sqrt{5\times 5\times 5\times 5\times 3\times 3} \\ \Rightarrow \sqrt{5625}=5\times 5\times 3 \\ \Rightarrow \sqrt{5625}=75 \end{gathered}$$

Hence, the square root of $5625$ is $75$.