In Exercises 11–28, add or subtract as indicated. You will need t...

Question

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals.
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5√12 + √75

Accepted Answer

Hey, everyone in this problem, we're asked to perform the addition of radicals. After simplification, the expression we're given is 13 multiplied by the square root of 72 plus the square root of 98. We're given four answer choices. Option A 14 multiplied by the square root of two. Option B 12 multiplied by the square root of two. Option C 71 multiplied by the square root of two. And option D 85 multiplied by the square root of two. Now we're gonna start by rewriting what we were given. So we have 13 multiplied by the square root of plus the square root of 98. Now the square root of 72 the square root of 98 those are not gonna give us nice integer values. OK? Which is what we want in order to simplify. So what we wanna do is we wanna try to break those factors up, OK? Into something that is going to give us an integer when we take the square root multiplied by something else that isn't OK. So that we can reduce those square roots and simplify. So we have 13 multiplied by the square root And 72 can be written as multiplied by two. And we know the square root of 36 is 6. And then we're left with just a square root of two. We also have the square root of 98. And we can write this as the square root of multiplied by two. OK. The square root of 49 we know is seven. And so this is gonna give us a way to simplify. So now we have the square root here, have two things multiplied together. How do we actually apply that square root? I recall if we have the square root of X multiplied by Y, we can write this as the square root of X multiplied by the square root of Y. So we can split them up, take the square roots first and then multiply the result together applying this to our problem. We have 13 multiplied by the square root of multiplied by the square root of two plus the square root of 49 multiplied by the square root of two. This gives us 13, the square of 36 is 6. So we have 13 multiplied by six, multiplied by the square root of two plus the square root of 49, which is equal to seven, multiplied by the square root of two, 13 multiplied by six. And that's equal to 78. So we get 78 multiplied. I have a square out of two plus seven multiplied by the square root of two. So 78 multiplied by the square root of two plus seven, multiplied by the square root of two gives us 85 multiplied by the square root of two. And that's our simplified expression. We can't simplify any further. We have a constant multiplied by the smallest route we can have here that doesn't give us a nice integer. And so we took our two terms, we had two separate terms with square roots and we were able to simplify it down into just one root and a constant. OK. If we compare this to our answer choices, we found the correct answer is 85 multiplied by the square root of two which corresponds to answer choice D. Thanks everyone for watching. I hope this video helped see you in the next one.

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In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. 5√12 + √75