In Exercises 65–70, perform the indicated operation(s) and write ...

Question

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form.

5√-16 + 3√-81

Accepted Answer

Hello everyone in this video we're gonna be looking at this practice problem where we need to simplify the expression three times the square root of negative 25 plus seven times the square root of negative 64. And we want to make sure to express our answer in standard form. So in this case you can see that we have negative values in the square root and whenever there is a negative value in the square root you should start thinking about Imaginary numbers or complex numbers because recall that the imaginary component I is equal to the square root of -1. And a complex number is just a combination of real part. A plus the imaginary part B. I. So we're gonna try to get these square roots to be negative ones. So we can express them using I So expression is three times the square root of negative plus seven times the square root of negative 64. And if I deal with just that first component three times the square root of negative I can rewrite it as three times the square root of negative one times 25. And then I can separate that square root into two parts. Where I'm left with three times the square root of negative one Times The Square Root of 25. And notice that five squared is equal to 25. So the square root of 25 can just be written as five. So I'm left with three times five Times The Square Root of -1. So I can write this as 15 times the square root of negative one. And remember that we said i is equal to negative one. So I'm gonna rewrite that square root of negative one as 15. I and then if I deal with my second component, seven times the square root of negative 64 I'm going to follow that same process that we did above where I do negative one times 64. And I'm left with seven times the square root of negative one times the square root of 64. And in this case notice that eight squared is equal to 64. So the square root of 64 is equal to eight. So I can write this seven times eight times the square root of a negative one. So I can write this as 56. I because recall that I is equal to the square root of -1. So now I have a value for both of my components. I'm gonna plug those back in. So three times the square root of negative 25 becomes 15 I and seven times the square root of negative 64 becomes 56. I And if I add these two values together, I'm left with 71, I notice that there's no real components. So I don't have to worry about writing my answer and standard form. So this becomes my final answer And you can see that eye is also answer choice c. So hopefully this video helped and see you next time.

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