Question

What is the square root of $3025$ by prime factorization?

Answer 1

Determine the square root of $3025$ by prime factorization.

The square root of a number is the value that returns the original number when multiplied by itself.

Find the prime factors of $3025$:

$3025=5\times 5\times 11\times 11$

Take the square root from both sides of the above equation:

$$\begin{gathered} \sqrt{3025}=\sqrt{5\times 5\times 11\times 11} \\ \Rightarrow \sqrt{3025}=5\times 11 \\ \Rightarrow \sqrt{3025}=55 \end{gathered}$$

Hence, the square root of $3025$ by prime factorization is $55$.