How do you simplify fractions with square roots?

1 Answer

See below:

Explanation:

Let's say I have:

52

How do I simplify this?

Remember that 2×2=2 And so if I can multiply the denominator by 2, we'll get 2 for the denominator. And that can be done, so long as we multiply both the numerator and denominator by the same thing (which means we're multiplying the fraction by 1 and not changing its value):

52(1)=52(22)=522

I can do the same type of thing if I have a mixed radical in my denominator. Let's say it's:

532

If I multiply two types of this kind of number, one adding the square root and the other subtracting, I can simplify. Let's look at our example again. With 32, we can multiply by 3+2:

(32)(3+2)=932+322=7

And so for the full fraction, we have:

532(3+23+2)=15+527