# How do you factor and simplify the square root of 75?

Apr 7, 2015

We have to first find the largest square factor in the number that you are square rooting.

$75 = 25$ x $3$

$25$ is a square number! $25 = {5}^{2}$

$\sqrt{75}$=$\sqrt{25}$ x $\sqrt{3}$

$\sqrt{75}$= $5$ x $\sqrt{3}$ = $5$$\sqrt{3}$

3 is a prime number and does not have any factors and thus the square root of 3 cannot be simplified further.