Simplify each radical. See Example 5.

3√27

Question

Simplify each radical. See Example 5.

3√27

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the radical expression. Five multiplied by the square root of 175. For our answer choices A is seven multiplied by the square root of five, B is five multiplied by the square root of seven C is 25 multiplied by the square root of seven and D is 125 multiplied by the square root of seven. Now, what we want to know, well, we want to simplify the radical expression and recall that when it comes to radicals, we know that the square root of a product that is a multiplied by B is the same thing as the square of a multiplied by the square root of B. So we have a term here 175. And if we can find a square factor from that term, we can simplify so that we can eventually write our radical expression with no square factors remaining under the radical. So let's think about it. What square number is in the product of the square root of 175? Well, 175 is actually equal to multiplied by seven and 25 is a square number. So applying our property of radicals, we know we can rewrite that as five multiplied by the square of 25 multiplied by the square root of seven, the square root of 25 is five. So we can rewrite that as five multiplied by five, multiplied by the square of seven and five multiplied by five is 25. Therefore simplified. Our answer is 25 multiplied by the spirit of seven, which is answer choice. C thanks a lot for watching everyone. I hope this video helped.

Simplify each radical. See Example 5. 3√27

Key Concepts

Radical Expressions

Properties of Exponents

Simplifying Radicals

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