Question

How do you simplify fractions with square roots?

Answer 1

See below:

Explanation:

Let's say I have:

`5/sqrt2`

How do I simplify this?

Remember that `sqrt2xxsqrt2=2` And so if I can multiply the denominator by `sqrt2`, 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):

`5/sqrt2(1)=5/sqrt2(sqrt2/sqrt2)=(5sqrt2)/2`

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

`5/(3-sqrt2)`

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 `3-sqrt2`, we can multiply by `3+sqrt2`:

`(3-sqrt2)(3+sqrt2)=9-3sqrt2+3sqrt2-2=7`

And so for the full fraction, we have:

`5/(3-sqrt2)((3+sqrt2)/(3+sqrt2))=(15+5sqrt2)/7`