First, simplify the fraction in the square root:

#sqrt(125/126)#

Then, use the rule#sqrt(a/b)=sqrt(a)/sqrt(b)#:

#sqrt(125)/sqrt(126)#

Now, onto simplifying the radicals on the top and bottom: split the square roots using the rule #sqrt(ab)=sqrt(a)*sqrt(b)#:

#(sqrt(25)*sqrt(5))/(sqrt(9)*sqrt(14))# (see notes below if this doesn't make sense)

Simplify #sqrt(25)# and #sqrt(9)#:

#(5*sqrt(5))/(3*sqrt(14))#

And that's as far as you can go!

**Note on simplification of #sqrt(125)# & #sqrt(126)#:**

The way I used to simplify these is to find all the prime factors:

#sqrt(125)= sqrt(5) * sqrt(5) * sqrt(5)#

#sqrt(126) = sqrt(2) * sqrt(3) * sqrt(3) * sqrt(7)#

Since #sqrt(5) * sqrt(5) = sqrt(5)^2 = 5# and #sqrt(3) * sqrt(3) = sqrt(3)^2 = 3#, you can simplify these to:

#sqrt(125)= 5 * sqrt(5)#

#sqrt(126) = sqrt(2) * 3 * sqrt(7)#

Using the rule #sqrt(ab)=sqrt(a) * sqrt(b)# on the second expression:

#sqrt(125)= 5 * sqrt(5)#

#sqrt(126) = 3 * sqrt(14)#

And you end up in the same place as the first method