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.

√25 + √64

Accepted Answer

Welcome back. I am so glad you're here. We're asked to perform edition without the use of a calculator. Our expression is the square rut of 256 plus the square root of 324. Our answer choices are answer choice. A 34 answer choice B negative two, answer choice C two square rut 145 and answer choice D two. All right. So we have two numbers both inside of radicals. We're asked to add them together, but we can only add radicals together if they have the same number on the inside. 256 is not the same as 324. So we can't add just yet, but we can see if there's anything we can pull outside of the radical that would maybe make them the same number on the inside. So looking at 256 you might know exactly what the square root of 256 is. But if you don't and you're not allowed to use a calculator, one thing you can do is build a factor tree to see what factors are on the inside. So taking 256. We know that's an even number. We can divide it by two and 256 divided by two is 128. Well, 128 still an even number. And that would be two multiplied by and 64. Hey, we know that 1 64 is eight multiplied by eight. So we see the factors here are two multiplied by two, multiplied by eight, multiplied by eight. And there are two twos and two eights. So we can combine 12 with 182, multiplied by eight is 16. And then combine the other two with the other 82, multiplied by eight is still 16 and 16, multiplied by 16 is the same as 16 squared. Well, the square rut of 256 is the same thing as the square rut of 16 squared. And when we take the square rut of a square, then it's just going to be that base number. So the square rut of 16 squared is just 16. Now, we can do the same thing for 324. We see that that's even. So that's two multiplied by 162. 162 is still even that one's two multiplied by 81 81 81 is nine multiplied by nine. So again, we've got two twos and this time two nines and we can combine a two and a nine, that's 18, combine the other two and the other nine, that's another 18, 324 is 18 squared. So when we're taking the square ret of 324 we're taking the square rut of 18 squared and the square of 18 squared is 18. So we're just taking 16 plus 18, which is a positive 34. And that's our expression simplified. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64

Key Concepts

Square Roots

Addition of Square Roots

Mental Math Techniques

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