In Exercises 1–3, perform the indicated operations and write the ...

Question

In Exercises 1–3, perform the indicated operations and write the result in standard form.    ___        ___2√−49 + 3√−64

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to 12 radical negative 81 plus 15 radical negative 196. Our answer choices are a 108 plus I B 318 I C 210 plus 108 I D negative rewriting my expression again, we have 12 multiplied by the square root of negative plus 15, multiplied by the square root of negative 196. I'm gonna go term by term in the first term, I'm bringing the 12 down putting a multiplication sign. And then I recall that I can break up a square root or a radical as long as I do so by multiplication. So the square root of negative 81 I can break down into the square root of negative one multiplied by the squared of 81. Since 81 is a perfect square, this will get rid of our radical. So going down, we have 12 multiplied by the square root of negative one which is I multiplied by the squared of 81 which is nine. So now we have the multiplication 12 multiplied by I multiplied by nine. So doing this multiplication out, I get 108 I, I'm gonna bring the plus sign between the two terms straight down. And then I'm gonna work with the term 15, multiplied by the square root of negative 196. Again, that number out front, I'm bringing it down as 15. And I'm gonna just put a multiplication sign next to it. I'm going to break down the square root of negative 196 into the square root of negative one multiplied by the squared of 196. I recognize that the squared of 196 is a perfect square. So this again will get rid of my radical, which is awesome. 15 stays 15. The squared of negative one is I and then the square root of 196 is 14. So we now have 15, multiplied by I multiplied by 14, which multiplies out to 210. I. So now to find our equivalent expression, we just need to add 108 I plus 210 I and when we do so we get 318 I, that is our equivalent expression and answer choice B have a nice day.

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In Exercises 1–3, perform the indicated operations and write the result in standard form. _ _2√−49 + 3√−64

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