Perform the indicated operations. Assume all variables represent ...

Question

Perform the indicated operations. Assume all variables represent positive real numbers. (√3 + √8)²

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression in parentheses. We have the square root of 23 plus the square root of 29 and that whole thing is squared. We are asked to simplify this expression and evaluate using exact values. So we recall from previous lessons that when we have something in parentheses squared, that's the same as taking what's in parentheses. So the squared of 23 plus the square root of 29 and multiplying it by itself. So again, times the square root of 23 plus the square root of 29. Now we will use the foil method to multiply these two sets of parentheses together. So we'll take the firsts from each set of parentheses, the square root of 23 and multiply them together, times the square root of 23. And once we've multiplied those together, we will add them to our outsides multiplied together. So that's the square root of 23 times the square root of 29. Those are our outsides. Once we multiply those, we add those to our insides multiplied together. Our insides here are the square root of times the square root of 23. Once we've multiplied those insides together, we add those to our lasts multiplied together. So in this case that's the square root of 29 times the square root of 29. Now let's go ahead and do that multiplication. So the square root of 23 times the square root of 23. I'm going to write that inside the radical as the square root of squared. Now for our Outsides, The squared of 23 times the square root of 29 while we take 23 times 29 that gives us 667. So we have the square root of 667. And for our insides we've got again 29 times 23 inside the radicals. So again, this is going to be the square root of 667. And then for our lasts, well we have the square root of 29 times the square root of 29. I'm going to write that as the square root of 29 squared. Now we can simplify, we know that the squared of 23 squared is just 23. We have two square roots of 667. That's like saying one squared of 667 plus another one squared of 667. And hey, we've got two square roots of 667 and this last here the square root of 29 squared is going to be 29. We have plus 29. Now we can combine like terms those are the ones without any radicals here. And that's going to be a 23 plus 29. Well that equals 52. So we have 52 plus two times the square root of 667 And 52 and to have a greatest common factor of two, so we can factor out a two and we do that. And 52 divided by two, leaves us with 26 plus two square root of 667 divided by two, leaves us with just the square root of And that's as simplified as this one can get. So we look at our answer choices for two times parentheses, 26 plus the square root of 667 and that matches with answer choice a well done, we'll catch you on the next one.

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Perform the indicated operations. Assume all variables represent positive real numbers. (√3 + √8)²