Rationalize each denominator. See Example 8.

18
——
√27

Question

Rationalize each denominator. See Example 8.

18
——
 √27

Accepted Answer

Welcome back. Everyone. In this problem, we want to rationalize the denominator of the radical expression 28 divided by the square root of 216. For our answer choices A is seven multiplied by the screw root of six, all divided by three B is nine, multiplied by the S root of six, all divided by seven C is seven multiplied by the screw of six, all divided by nine. And the D is 14 multiplied by the screw root of six all divided by three. Now, if we're going to rationalize our radical expression, the denominator of the radical expression, that is, it would be easiest to do it if our radical expression is in its simplest form. In other words, we want to rewrite our radical expression in such a way that there are no square factors for that number are under the RAA. So let's think about it. What square number is a product of 200 is a part of the product of 260? Well, to help us, let's recall the product rule of radicals that says that the radical of a product A B equals the radical of a multiplied by the radical of B. And when we think about it, 216 is actually equal to 36 multiplied by six. So we can rewrite our denominator as the square root of 36 multiplied by six, where 36 is a square number. If we take it a step further, by applying the property that can be written as 28 divided by the spirit of 36 multiplied by the spirit of six. No, the square root of 36 equals six. So I can write that as 28 divided by six multiplied by the square root of six, we can even take it a step further because 28 and six are even numbers. And if we divide both by two, if we factor 02, 26 goes three times, 2028 goes 14 times. So I can rewrite it as 14 divided by three multiplied by the square of six. Now six has no square factors. So now I know that my radical is in its simplest form. No, we can rationalize. What does that mean? Well, to rationalize just means that we need to think of a number that we can multiply three multiplied by the spirit of six by to get rid of that radical. The spirit of six. What number do you think that is? Well, the easiest number is likely the square of six. But if I multiply the denominator by the square of six, I'd have to do the same to the numerator to keep its value. No, when we rewrite that the numerator will be 14 multiplied by the square root of six. And in our denominator, we will have three multiplied by the square of six, multiplied by the square of six, which would just be equal to three multiplied by six, three multiplied by six equals 18. And again, looking at our expression two is a common factor of 14 and 18. So in a factor two, from both 2 to 14 goes seven times 2018 goes nine times. So our final answer would be seven multiplied by the spirit of six, all divided by nine. When we look back 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. 18 —— √27

Key Concepts

Rationalizing the Denominator

Properties of Square Roots

Simplifying Radicals

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