About rationalizing denominator, is it true that you can't always multiply by the same square root denominator to get a perfect square?

Answer 1

yes, because (√n)² = n

so, multiplying the root by itself gets rid of the root.

If the denominator is not just a root, but something like √m + n, then you need to multiply by √m - n, since

(√m + n)(√m - n) = m - n²

also, you sometimes have to use

(√m + √n)(√m - √n) = m - n