# How do you simplify #sqrt(75a^12b^3c^5)#?

##### 1 Answer

Feb 4, 2015

We'll need a few properties.

- First of all, let's recall that
#\sqrt{a\cdot b}=\sqrt{a} \sqrt{b}# . This of course applies also to products of more than two factors. - I hope you will be ok with the fact that the square root of a number is that number to the power of
#1/2# . If not, tell me in the comments and I will explain this exercise in another way. - The third properties is that
#a^{b+c}=a^b\cdot a^c# .

If this things are ok, for the first point we can separate the roots:

Factoring

For

For

For

Putting all the pieces together, we have that