A: There are a few ways to do this, but first I will rationalize the denominator (that means get rid of the square root in the denominator) and then I will simplify the square root (simplest radical form):
Step 1: Rationalize the denominator:
Multiply the top and bottom by sqrt(75):
Now, simplify algebraically:
Simplify the denominator to get 150… for some reason, I can’t make my picture keep it in a fully fraction with 150 in the bottom, so the image shows the 150 pulled out like so (either way is fine):
Now reduce the 15 and the 150 to get:
The denominator has been rationalized (no square roots in the denominator) and the fraction has been reduced.
Step 2: Put the numerator into simplest radical form:
To go to simplest radical form, you want to see what “perfect squares” divide into the square root. So, what perfect squares divide into 75? 25 is a perfect square that divides into 75: 3*25=75.
So, we can break up the square root like so (again, the square roots can be on top of the fraction, just having image problems):
Now, what is the square root of 25? That’s 5, so simplify:
And, now reduce the fraction part of the 5 and the 10 in the denominator to get:
You are done!