Simplify. See Example 9.

- √2
3
———
√7
3

Question

Simplify. See Example 9.

- √2
 3
———
 √7
 3

Accepted Answer

Welcome back. Everyone in this problem, we want to simplify the expression of the negative value of the Spirit of 17 divided by five all divided by the Spirit of 19, divided by five. For our answer choices. A is the Spirit of 17 divided by 19 B is a negative value of five multiplied by the Spirit of 17, all divided by 19 C is a negative value of the square root of 323 divided by 19 and D is the square root of 323 divided by 19. Now, what do we know here? Well, here we have a quotient that has one fraction being divided by the other. So before we start to simplify, the best thing would try, would be trying to rewrite this as one quotient. So let's see if we can do that. So we're working with the square root of 17 divided by five, divided by the square root of 19, divided by five. And remember we're finding the negative value for all of that, we can rewrite this as the negative value of the square root of 17 divided by five multiplied by five divided by the square root of 19, both have a common factor of five. And when we factor five out, we're left with the negative value of the square root of 17 divided by the square root of 19. No, it's one term. It's a single quotient. So we've been doing good so far, but it's still not in its simplest form. And that's because a radical is in the denominator. So to get it even simpler, we can rationalize our denominator to get rid of the radical. Now, let's think to rationalize what can we multiply the square root of 19 by to get rid of the square root? Well, we could multiply it by the square root of 19. But if we multiply the denominator by the spirit of 19, we'll have to multiply the numerator by the same value. So when we compute what we have here, it will be the negative value of the square root of 17 multiplied by the square root of 19, divided by the square root of 19 multiplied by the square root of 19, which just equals 19. Now, we can even take this a step further because notice here, we're multiplying two radicals and recall that the product rule of radicals tells us that when we're multiplying two radicals, it's the same thing as finding the radical of their product. So that means I can rewrite my numerator as the square root of 17 multiplied by 90 no, 17 multiplied by 19 equals 323. So I'm finding the square root of 323 divided by 19. Since there are no square factors of 323 that means it's written in its simplest form. So my final answer is the negative of the square root of 323 divided by 19. And when we look back on our answer choices that would have been answer choice. C Thanks a lot for watching everyone. I hope this video helped.

Simplify. See Example 9. - √2 3 ——— √7 3

Key Concepts

Rationalizing the Denominator

Simplifying Radicals

Fraction Operations

Watch next