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 a radical expression. The square root of 961 were to indicate if this route is a real number and if it is real to evaluate. So let's look inside the radical that is a positive a non negative real number. So we can go ahead and evaluate it. So when we've got a number like 961, that isn't very intuitive. If we know that that's got a real square root one, you could just go into your calculator and type squirt of 961. But if you don't have a calculator available, what you'll want to do is make a factor tree for this number and you want to know what the indexes. There's an unspoken to here and it means that you want to look for factors that come in pairs of two so that those can come out of the radical. And for an unusual number, you want to look at the last digit and you want to say, well what time is what can multiply together to also end in that same digit? So in this case what times what multiplies together to equal something that ends in a one? Well three times seven. Those equal 21. Does three go into 961? No, Does a seven go into 961? No. Well what else multiplies together and ends in a one. Well nine times nine is 81 but no nine doesn't go into 961. How about 11? No, 11 doesn't go into 961. Well now, at this point you can just keep trying numbers that end with these 137 and nine and you can keep going and eventually you'll hit on 31 and you'll find that 31 does go into 961. It goes in 31 times, and so therefore squared equals 961. So when we take the square root of 31 squared, well, that just leaves us with 31 which matches our answer choice C Well done, we'll catch you on the next one.

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