Question

Rationalize the denominator and simplify.

Answer 1

To rationalize the denominator we have to get rid of the square roots in the denominator.

The way to do that is to multiply it by its conjugate. And we have to multiply both the numerator and denominator with it! This is important because we're essentially multiplying it by 1 so we're not changing the value of it.

So what is a conjugate?

The conjugate in this case is going to be the same thing except you switch the sign.

So if you had a+b, the conjugate would be a-b
If you have a-b, the conjugate is a+b

What is the conjugate of \( 4\sqrt{6} - 3\sqrt{2}\) ?