Find each product or quotient. Simplify the answers. √-10 / √-...

Question

Find each product or quotient. Simplify the answers. √-10 / √-40

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression, we have the square root of negative 17 divided by the square root Of -119. And were to determine the quotient essentially to do the division here. We've got a couple of things to take note of. We are taking the square root of some negative numbers. We cannot do that and we have a root in our denominator. We cannot have that either. So let's address the taking the square root of a negative first. Let's rewrite these. As in the numerator we have the square root of negative one times 17. And in the denominator we have the square root of negative one times 119. And taking a look at these square root of negative one. We know from previous lessons that by definition the square root of negative one is equal to I. So we can pull an eye out of both of those. So in the numerator will have I times the square root of Divided by and in the denominator we have i times the square root of 119. So now we have I divided by eye and those will cancel out. So that's helpful. And now we still have that ready for that radical in our denominator. So we want to move that out of there. We need to do that by Having two of any factor that is inside of the radical. We know from this unwritten index of two for our square root 119 is the same as 17 times seven. Neither of those are repeated. So we're going to need to multiply this whole thing times another square root of 119 to get another 17 and another seven in there. And what we multiply the denominator by. We need to multiply the numerator by as well. So we'll be taking in the numerator And I'll just keep these as factors. For now we have the square root of 17 and then that's times 119, which we know is 17 times seven. And then in the denominator we have the square root of times seven which is 100 and 19 times 17 times seven. So we will be able to take out in our denominator will be able to take out a 17 and a seven and those multiplied together. Those are just 119 in our denominator. But we could keep that as 17 times seven as well. In our numerator we have 2 17. So 17 can come out, that would be 17 and then that square root of seven has to stay in there. This is where it's a little bit more helpful to keep it written as factors because when we look at 17 squared of seven divided by 17 times seven, it's clear that we can cancel out these 17 factors here. And that leaves us with the square root of seven divided by seven as a final answer. We look at our answer choices and the square root of seven, divided by seven matches with answer choice D. Well done, we'll catch you on the next one.

Find each product or quotient. Simplify the answers. √-10 / √-40

Key Concepts

Simplifying Square Roots of Negative Numbers

Properties of Radicals in Division

Simplifying Radicals by Factoring

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