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. −√36

Accepted Answer

Welcome back. I'm so glad you're here. We've got this radical expression negative square root of 841. And we want to find out if this is real. And if so can we evaluate it? Well the negative is on the outside of the radical. Inside that radical. It's just a non negative, it's a positive real number. So we can go ahead with this. And if you've got a calculator and you want to plug in the square root of 841, great. If you don't have access to a calculator and you're trying to figure out how to break this down. Well what you want to do is you want to look at the index. The index here is an unwritten too. And then you want to build up a factor tree for the number in there. And you want to find out if there are any factors that come in twos that could then come out of the radical. And when you've got something that isn't super intuitive like 841, you want to look at the last number in this whole number and you want to say what times what ends are, gives us an answer that ends with that. So what times what gives us an answer that ends with one? Well three times seven that gives us 21. So you can check 841 divided by three. It doesn't go into it evenly. 841 divided by seven. It doesn't go into it evenly. What else multiplies and gets us something that ends in a one, Well nine times nine is 81 But nine doesn't go into 841. What about 11 times something? No. 841 isn't evenly divided by 11. So you can just keep going with these and trying different numbers that end with these other numbers here on our list. And eventually you'll find that does go into 841. And it just so happens that 29 times Or 29 squared is 841. So when we take the square root of 29 squared, that gives us 29 we bring down that negative in front of it. And that gives us an answer of -29 which matches with answer choice. A well done. We'll catch you on the next one.

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