How to Simplify Radical Expressions by Rationalizing the Denominators

Hi, I'm Rachel, and today we're going to be going over how to simplify radical expressions by rationalizing the denominator. If we're given an example such as five over the square root of nine, we know that we can never have a square root in the denominator. So we have to rationalize it. We cannot write this radical expression as such. So, what we do is multiply what we have in the denominator by itself to get rid of the square root. If we multiply it by the square root of nine, the square root of nine from the square root of nine is nine, right? That's the square root of nine-squared, which is nine. So that's gonna be nine on the bottom. But we can't just multiply the denominator by the square root of nine, we have to multiply the numerator by it as well so that we're actually really just multiplying this fraction by a version of one. Square root over nine over square root of nine is one, so we can multiply anything by one and it stays the same, it keeps its identity. So, we can by the rules of math multiply this by the square root of nine over the square root of nine, we get nine on the bottom, which is great, no more square root, and now we have five times the square root of nine on the top, which we just write as five root nine. And now we've solved for it, and there's no way more to simplify, but this is an okay form to write this radical expression because there's no square root in the denominator, it's only in the numerator where it's allowed. And now we've simplified the radical expression. I'm Rachel, and thank you for learning with me today.