Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16

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Welcome back. I'm so glad you're here. We've got this radical expression, we've got the square root of 900 minus the square root of 841. We're supposed to figure out if it's real and evaluate, well we've got non negative real numbers inside of our radicals. So looks like we're good to go and try and evaluate if you've got a calculator and you can just plug in the squared of 900 Great or the squared of 841 great. You can plug those in. If you don't, then we can take some steps to figure that out. Simplify it. We want to find out if there are any factors of the number inside the radical that come in pairs of two. So we can do a factor tree for 900 And we can say, well what times, what is 900? Well 100 times nine is 901 100 is the same as 10 times 10 and nine is the same as three times three. And look at that, there's two pairs right there, 10 squared times three squared. And actually we can go ahead and multiply 10 squared times three squared. And that equals 30 squared. So we know that 900 can also be rewritten as 30 squared And the square root of 30 squared is 30. So we've got that first one simplified, you calculator. People have that way before us and now we look at and see are there any factors that come in twos that can come out of 841? So we can start a factor tree for that. And you want to look at this last number here when it's not super intuitive what goes into 841? I don't know. But we know that things multiplied that end in one, for instance, three times seven. So three could go into this hint, it doesn't A seven could go into this hint. It doesn't. Well what else? Multiplies and ends in a 19 times nine, Hint. It doesn't go into 841. But um an 11 that could No it doesn't go into this one. Okay, you can keep going and keep trying different numbers that end in these and keep going and eventually you will find out that 29 times 29 gives us 841. So in other words, 29 squared is 841. And when we want to take the square root of 29 squared, well that's 29. Now we can take 30 minus 29 that gives us one which matches with our answer choice. B While done, we'll catch on the next one

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16

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Key Concepts

Square Roots

Real Numbers

Simplifying Expressions