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

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Answer 1 · 2018-06-10T23:58:09

#2/5#

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!