Simplify each radical. See Example 5.

- √160

Question

Simplify each radical. See Example 5.

- √160

Accepted Answer

Welcome back everyone. In this problem, we want to simplify the radical expression of the negative of the square root of 490. For our answer choices A is negative seven multiplied by the square root of 10, B is negative seven C is negative and D is negative 10. Now, what do we already know here? Well, we're trying to simplify our radical expression. And what that means is that we want to rewrite our radical where there are no more square factors left under the radical. We also know that the radical of our product A B equals the radical of A multiplied by the radical of B. So if we can use that property to help us, we can find the square root of our square factor in the radical. So let's think about it. Are there any square factors that we can multiply by to get 490? In other words, are there any square numbers in the product of 490? Well, since we're looking here, notice that we can rewrite 4 90 as 49 multiplied by because 49 is a square number and by applying our property of radicals. We can rewrite that as the square of 49 multiplied by the square root of 10. We know the square of 49 is seven and we can rewrite the script of 10. And remember we're finding the negative of all that. Therefore, our answer is negative several multiplied by the script of 10, which when we check our answer choices that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

Simplify each radical. See Example 5. - √160

Key Concepts

Radical Simplification

Perfect Squares

Properties of Radicals

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