Question

What is the square root of $105$?

Answer 1

Determine the square root of $105$

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

Prime Factorize the given number:

$105=3x5x7$

Take the square root from the above equation:

$$\begin{gathered} \sqrt{105}=\sqrt{(3\times 5\times 7)} \\ \Rightarrow \sqrt{105}=\sqrt{3}\times \sqrt{5}\times \sqrt{7} \\ \Rightarrow \sqrt{105}=1.732\times 2.236\times 2.646 \\ \Rightarrow \sqrt{105}=10.246 \end{gathered}$$

Hence, the square root of $105$ is$10.246$.