Question

Find the square root of $6084$ by prime factorization method.

Answer 1

Step 1: Find the prime factors

The prime factors of $6084$ are

$6084=2\times 2\times 3\times 3\times 13\times 13$

Step 2: Find the square root

The square root of $6084$ is

$$\begin{gathered} 6084=2\times 2\times 3\times 3\times 13\times 13 \\ \Rightarrow \sqrt{6084}=\sqrt{2\times 2\times 3\times 3\times 13\times 13} \\ \Rightarrow \sqrt{6084}=2\times 3\times 13 \\ \Rightarrow \sqrt{6084}=78 \end{gathered}$$

Hence, the square root of $6084$ is $78$