Use the quotient rule to simplify the expressions in Exercises 23...

Question

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1

Accepted Answer

welcome back. I'm so glad you're here. We have this expression we have the square root of 490 H. To the fifth divided by the square root of five H. To the negative third and we are to simplify this using the quotient rule. Well what is the quotient rule? We recall from previous lessons that when we have the square root of a divided by B. That's the same as the square root of a, divided by the square root of B. And since they're both equal, it works from right to left as well. We can take the squared of something divided by the squared of something and change it to the square root of the whole thing. So in this case we will now take the square root of 490 H. To the fifth divided by five H. To the negative third. And now we can do the operations in here, we can take 490 divided by five and that is 98. So this is still inside the radical. So we've got the square root of 98 And we've got that age to the 5th and that H. To the negative third in the denominator, will that negative exponent tells us that it needs to flip up to the numerator to make that exponent positive. So that will be H. To the fifth times H. To the third and we can go ahead and combine that age to the fifth H. To the third. This will be the squared of 98. And because they're being multiplied we're going to add the exponents. So it's 98 H. To the eighth. Now we want to see what we can get out of the radical. Well if we're looking at 98 we make a factor tree, we know that's divisible by two and that happens to be two times 49 49 is seven times seven. So this 98 is seven squared times two. And we can actually think of age to the eighth. Like a factor tree to H. To the eighth is the same as H. Two. The fourth times H. To the fourth which is H. Two, the fourth squared. So now we can rewrite this as the square root of seven squared times two times each to the fourth squared. And we know that anything that is squared inside of that square root gets to come out and it's thrilled as it comes outside of the square root bracket, it gets reduced. So the square root of seven squared is just seven. The square root of H. Two, the fourth squared is just H. Two the fourth and left inside this lonely radical is still the square root of two and that's as simplified as it's going to get we look at our answer choices and that matches answer choice. C. Well done, we'll catch you on the next one

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1

Key Concepts

Quotient Rule

Radical Expressions

Simplifying Expressions

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