# How do you simplify 3sqrt175?

Mar 28, 2018

Pull out as much of the value that's under the radical as possible. You'll find that the simplified version is $15 \sqrt{7}$

#### Explanation:

What I did was look for factors of the term underneath the radical (175) that were a perfect square.

I found that the largest term that fits the description is 25. I used that in the expression to simplify the expression:

$3 \sqrt{175} = 3 \sqrt{25 \times 7} = 3 \sqrt{25} \sqrt{7}$

$3 \sqrt{25} \sqrt{7} = 3 \times 5 \sqrt{7}$

$\textcolor{red}{\Rightarrow 15 \sqrt{7}}$

Mar 28, 2018

15$\sqrt{7}$
175 = 7 x 25 so $\sqrt{175}$ = $\sqrt{7}$x $\sqrt{25}$ or $\sqrt{7}$$\sqrt{25}$
so $3 \sqrt{175}$ can be written 3$\sqrt{7}$$\sqrt{25}$
as $\sqrt{25}$ = 5 then 3$\sqrt{7}$$\sqrt{25}$ = 15$\sqrt{7}$