Rationalize the denominator.

Question

$\frac{\sqrt{2}}{\sqrt{5}}$

Accepted Answer

Hello, today we are going to be rationalizing the denominator of the radical expression. The radical expression given to us is the square root of seven divided by the square root of 37. So how can we rationalize a denominator? While in order to rationalize a denominator, we want to simplify the denominator in a way that allows us to remove the square root symbol. Recall that the square root symbol allows us to simplify perfect squares into individual terms. So if we have the square root of 37 in the denominator, we can multiply the square root by itself in order to eliminate the square root symbol. But if we multiply the denominator by the square root of 37 we must also multiply the numerator by the square root of 37. So let's go ahead and take the products of the numerator and denominator. In the numerator, we will have the square root of seven multiplied by 37 which will give us the square root of 259. And in the denominator, we will have the square root of 37 multiplied by the square root of 37 which will simplify to give us the square root of 37 squared. Notice that in the denominator, we have a perfect square inside the square root symbol using the property that I stated in the upper right. We can simplify this denominator to just be 37. So we are left with the square root of 259 divided by 37. This is going to be the simplest form of the given rational expression with a rationalized denominator. And with that being said, the solution to this problem is going to be c 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.﻿25\frac{\sqrt{2}}{\sqrt{5}}5​2​​﻿

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Rationalize the denominator.
$\frac{\sqrt{2}}{\sqrt{5}}$