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

Question

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

5
√ ---
3

Accepted Answer

Hello, today we're gonna be rationalizing the numerator of the following expression. So what we are given is the square root of the quantity 13/6. Now we have a property for square roots that states that if we have the square root of A over B, we can rewrite this rational quantity as a square root over a square root. Or in other words, the square root of A over B can be rewritten as the square root of A over the square root of B. And if we apply this property to the current expression, we can rewrite the current expression as the square root of 13 over the square root of six. Now keep in mind the instructions tell us that we want to rationalize the numerator. And what that means is that we want to rewrite the numerator without the square root. So we need to multiply the numerator by a quantity that's going to allow us to eliminate the square root. And in this case here, let's go ahead and multiply the numerator and denominator by the square root of 13, the square root of 13 times the square root of 13 is going to give us the square root of 13 squared and the square root of six times the square root of 13 can be simplified to give us the square root of six times 13. Now, in the numerator, the squared of 13 squared is going to simplify to just give us 13. And in the denominator, the squared of six times 13 can be simplified to give us the square root of 78. 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 a. 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. 5 √ --- 3

Key Concepts

Rationalizing the Numerator

Simplifying Fractions

Square Roots and Their Properties

Watch next