Rationalize the denominator.

Question

$\frac{1}{\sqrt7}$

Accepted Answer

Hello, today we are going to be rationalizing the denominator of the radical expression. The radical expression given to us is one divided by the square root of 210. Now, what does it mean to rationalize the denominator? What it means is that we want to simplify the denominator in a way that it doesn't have any more square root terms. Or in other words, we want to remove the square root symbol from the denominator. So how do we start this process? Well, recall that the square root simplifies perfect squares. So for example, if we have the square root of a squared, this will simplify to give us a, this is useful to us because this tells us if we take the square root of 210 and multiply it by itself, this should simplify to give us 210. So we will take the square root in the denominator and multiply it by itself. But if we multiply the denominator by the square root of 210 we must also multiply the numerator by the square root of 210. So what we need to do is, we need to simplify one multiplied by the square root of 210 will give us the square root of 210 in the numerator. And in the denominator, the square root of 210 multiplied by the square root of 210 will give us the square root of 210 squared. Using this property, we can simplify the denominator to just be 210. And the expression can be simplified to be the square root of 210 divided by 210. This is going to be the simplest form of the radical expression with a rationalized denominator. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to rationalize a denominator. And I'll go ahead and see you all in the next video.

Rationalize the denominator.
$\frac{1}{\sqrt7}$

Key Concepts

Rationalizing the Denominator

Irrational Numbers

Multiplication of Fractions

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