CONCEPT PREVIEW Perform the operations mentally, and write the an...

Question

CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps.

√6 • √6

Accepted Answer

Welcome back. I am so glad you're here. We are asked to perform multiplication without the use of a calculator. We have the square of 31 multiplied by the square of 31. Our answer choices are answer choice, A two square at 31 answer choice B the square of 62 answer choice C one and answer choice D 31. All right, there are a few different ways that we can think about this one. First way I'm going to talk about, we have the same number, the square of 31 and the square root of being multiplied by itself. And when we have a number being multiplied by itself, we can say that that number is squared. So we say that the square root of 31 is being squared. Now, with that said, once we have the square root of something squared, the square root and the squared are essentially operations that are undoing each other. And so this just simplifies to a positive 31. Now, another way we could think about this knowing that we've got the square rut of 31 squared, we can also express the square rut of 31 as 31 raised to the one half power. And we know that that is being raised to the second power. We recall from previous lessons, the power to a power rule where one half being raised to the second power would mean we're going to multiply those two exponents and one half multiplied by two is a positive one. So we have 31 raised to the first power. Well, 31 raised to the first power is just 31. So there's a couple of different ways to think about this one. But the answer is 31. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6

Key Concepts

Square Roots

Multiplication of Square Roots

Properties of Exponents

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