Rationalize each denominator. See Example 8.

12
——
√72

Question

Rationalize each denominator. See Example 8.

12
——
 √72

Accepted Answer

Welcome back. Everyone. In this problem, we want to rationalize the denominator of the radical expression 27 divided by the square root of 486. For our answer choices, A is the spirit of six divided by three, B is the skirt of three divided by two C is a skirt of six divided by two and D is a spirit of two divided by six. Now, what do we already know? Well, we want to rationalize our denominator. But before we do that, it would be best to rationalize it if it's in its simplest form. So let's ask ourselves is the square root of written as the simplest radical possible. Well, not really because 486 has square factors. Recall that if we have a radical with square factors, the square root of A B, we can rewrite it as the square of a multiplied by the square root of B. So we can use that to simplify the ret of 486 1st and then we'll go ahead and rationalize. So let's ask ourselves what square factor is a part of 486 in other words, what square number is a part of the product that gives 486. Well, if we think about it, 486 is actually equal to 81 multiplied by six and 81 is a square number. So now that we have that we can apply the property and rewrite it as 27 divided by the square root of 81 multiplied by the square root of six. The skirt of 81 is nine. So I can rewrite this as 27 divided by nine multiplied by the spirit of six. We can even simplify it further because nine is a factor of 27 and nine into nine goes 19 into 27 goes three. So my ca can be rewritten as three divided by the square root of six, no six has no square factors. So we're sure that our radical is not in its simplest form now that we have that we can rationalize. What does that mean? Well, it just means that we want to multiply our caution by some value that will get rid of the radical in the denominator. So let's think what can we multiply the square root of six by to make it an integer? Well, the easiest answer would be to multiply it by the square root of six. But to keep the same value of the expression, I'd also have to multiply the numerator by the square of six. No, I can rewrite all of that as three multiplied by the square of six, divided by the square of six multiplied by the square of six, which just equals six. We can simplify even further. Given three is a factor of 63 goes into 31 time three goes into 62 times. Therefore, my final answer would be the square of six divided by two. And when we look in our answer choices, that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped.

Rationalize each denominator. See Example 8. 12 —— √72

Key Concepts

Rationalizing the Denominator

Square Roots

Multiplying by Conjugates

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