Multiply. See Example 7.

√6 (3 + √2)

Question

Multiply. See Example 7.

√6 (3 + √2)

Accepted Answer

Hello, everyone. We are asked to simplify the following expression, the squared of three multiplied by the parentheses five plus the squared of 15. Our answer choices are a five radical three plus three radical 15 B five radical three plus three radical five C six radical three plus three radical six D three radical three plus five radical six. First, I'm gonna rewrite the expression. So I have the square to three also known as radical three multiplied by the parentheses. Five plus the square to 15. We'll be using the distributive property to start with. So we will do the squared of three multiplied by five. And we're in treat square of three very much like a variable here. Since five does not have a square root, we can't combine them, but we can write them next to each other. So this would be five multiplied by the square to three or five radical three and then the square to three multiplied by the square to 15. Since they are both square roots, we can keep the square root symbol and multiply what's under it three multiplied by 15 is 45. So at this step, I have five radical three plus the square into 45. I'm looking to see if I can simplify anything. And I noticed that the square root of 45 does have a perfect square that I can factor out of this. So recall that when you simplify radicals, you look for a perfect square. So 45 is the same as nine multiplied by five. So I can break this down into factors. So the squared of 45 is the same as the squared of nine multiplied by the squared of five. The squared of nine is three, the square to five stays the square to five. So when I put this back together, I get three radical five. So I'm gonna go plug that back in for the square of and see if I've hit my simplified expression. So I'll have five radical three plus three radical five. And there's nothing more I can do here because they have different numbers under the square root symbol. So this is my answer answer. Choice B five radical three plus three radical five have a nice day.

Multiply. See Example 7. √6 (3 + √2)

Key Concepts

Distributive Property

Simplifying Radicals

Combining Like Terms

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