How do you simplify #sqrt(12/75)#?

1 Answer
Jun 10, 2018

Answer:

#2/5#

Explanation:

We can leverage the radical property

#sqrt(a/b)=sqrta/sqrtb#

All this is saying is that the square root of the quotient is the same as the quotient of the square roots. We can now rewrite our expression as

#color(blue)(sqrt12)/color(purple)(sqrt75)#

This is equivalent to

#color(blue)((sqrt4*sqrt3))/color(purple)((sqrt25*sqrt3))#

Since we have a #sqrt3# on the top and bottom, these cancel:

#(sqrt4*cancel(sqrt3))/(sqrt25*cancel(sqrt3))#

And we're left with

#sqrt4/sqrt25#

Which simplifies to

#2/5#

Hope this helps!