In Exercises 45–66, divide and, if possible, simplify.
___
√200
√...

Question

In Exercises 45–66, divide and, if possible, simplify.
___
√200
√10

Accepted Answer

Welcome back. I am so glad you're here. We're asked for the following expression, perform division and further simplify if possible. The expression we're given is in the numerator, the square root of 800. And that's divided by, in the denominator, the square root of 20. Our answer choices are answer choice, A two square at 10, answer, choice B two square at five, answer choice C four square at 10 and answer choice D four square at five. There are actually several ways to solve this problem. Um We note that we could start simplifying our numerator and our denominator and figure out what the square it of 800 the squared of are. However, we also recall from previous lessons that when we're taking the rut of both our numerator and our denominator, and they're the same rut. In this case, the squared rut, we can take the rut of the entire thing. So we can take The square root of the fraction. Our numerator is 800 and the denominator is 20. And now we can do the division inside of our radical 1st 800, divided by 20 equals 40. So this is equal to the square root of 40. And now we can simplify the square root of 40. We could say that 40 is the same as the factors four multiplied by 10. So putting that inside the radical, the square root of four multiplied by 10. We recall from previous lessons, that's the same as the square it of four multiplied by the square root of 10. And we can take the square root of four, the square of four is two. So this is equal to two square root 10, We can't simplify the square it of 10 because 10 is just two multiplied by five, it doesn't have two of any factor. So 10 cannot come out. And two square at 10 is as simplified as this one gets. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 45–66, divide and, if possible, simplify. ___ √200 √10

Key Concepts

Radical Expressions

Simplifying Radicals

Division of Radicals

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