Simplify each radical. See Example 5.

√24

Question

Simplify each radical. See Example 5.

√24

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the radical expression of the square root of 90. For our answer choices A is 30 B is three multiplied by the square root of 10 C is three and D is 10 multiplied by the square root of three. Now, what are we trying to do here? We want to simplify our radical expression. And that means we want to rewrite it in such a way that there are no more square factors left under the radical. We also know that for the radical of our product, the square root of A B, it's the same thing as the square of A multiplied by the square of B. So we want to see how we can use that property to help us to rewrite 90 as a product of a square factor and another number. So let's think about it. What square number can I multiply by to get the product of 90? Well, if we can recall 90 equals nine, multiplied by 10, 90 isn't a square number but 90 is well, nine is my, my apologies. So that means we can rewrite this as the square root of nine multiplied by 10. And by applying our property, we can further rewrite it as the spirit of nine multiplied by the square of 10. The spirit of nine equals three, 10 is not a square number. So my final answer would be three multiplied by the squared of 10, which when you look in our answer choices, that would be answer choice. B thanks a lot for watching everyone. I hope this video helped.

Simplify each radical. See Example 5. √24

Key Concepts

Radical Simplification

Perfect Squares

Prime Factorization

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