Evaluate each expression in Exercises 1–12, or indicate that the ...

Question

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25

Accepted Answer

Welcome back. I'm so glad you're here. We've got this radical expression. We have this square root of parentheses. 149 plus 107. We are to figure out if this is a real number or not. And if so evaluate. So inside those parentheses, those are like terms we can add 149 plus 107. That gives us 256. So we're looking at the square root of 256 which is a non negative number. So yeah, this is a real route. Now if you've got a calculator, you go ahead and plug in the squared of 256 you're going to be done much quicker than me. I'm going to show you what to do. If you don't have a calculator, you can always make a factor tree for some of these numbers that aren't quite as intuitive. It's like, I don't know this word of 256. So let's find out what it's factors are well, we know it's divisible by two because it's an even number and it's going to be two times 128 which is still even. So that's going to be two times well 64 64 still even that's two times 32 32 is two times 16. 16 is two times 88 is two times four and four is two times two. That's a lotta two. Let's count how many?  aN:aN:000NaN 12345678. So this number. 256. That's two to the eighth power. So we can write the square root of two to the eighth power. And now we know that to get out of the radical. We look at this index and when it's not written then it's just going to be two and we're going to take our exponent inside the parentheses to the eighth. We're going to divide that by two in order to get it out of the radical. So two to the eighth divided by two is two to the fourth power. And you can go ahead and multiply, you can take two times two times two times two and that's going to get you 16. So two to the fourth is 16. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

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