In Exercises 93–104, rationalize each numerator. Simplify, if pos...

Question

In Exercises 93–104, rationalize each numerator. Simplify, if possible.

√x + 4 
√x

Accepted Answer

Hello, today we're gonna be rationalizing the numerator of the given expression. So what we are given is the square root of H plus three over the square root of H. Now, since we want to rationalize the numerator, what this means is that we want to rewrite the numerator without the square root. In order to do this, we're gonna multiply the numerator and denominator by the opposite of the numerator. So in the numerator, we have the squared of H plus three and the opposite of this quantity is going to be the squared of H minus three. And we're gonna multiply this quantity to both the numerator and denominator. So let's go ahead and simplify the numerator and denominator individually. In the numerator, we have the quantity squared of H plus three multiplied by the squared of H minus three. In order to simplify this, we're going to foil the two quantities together. So we're going to take the first term of the first group and distribute it to each term in the second group. So the squared of H times the squared of H is going to give us the square root of H squared and the squared of H times negative three is going to give us negative three square root of H. Then we're going to repeat this process with the second term in the first group and distribute it to each term in the second group. So the square, so three times the squared of H is going to give us positive three squared of H and three times negative three is going to give us negative nine. Now, we're going to simplify negative three squared of H plus three squared of H is going to cancel each other L and the square root of H squared is going to simplify to give us H. So the numerator is going to simplify to give us H minus nine. Now let's go ahead and simplify the denominator in the denominator, we have the squared of H multiplied by the squared of H minus three. In order to simplify this, we're going to distribute the square of H to each term in the group. And the square root of H times A squared of H is going to give us the square root of H squared and the squared of H times negative three is going to give us negative three square root of H square root of H squared is going to simplify to give us H. And what we are left with in the denominator is H minus three times the square root of H. Now that we have the simplified forms of the numerator and denominator, let's put it back into the original expression. So in the numerator, we're going to have H minus nine and in the denominator, we're going to have H minus three square root of H and this is going to be the rationalized form of the given expression. And with that being said, the answer to this problem is going to be C so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x

Key Concepts

Rationalizing the Numerator

Simplifying Radicals

Algebraic Fractions

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