In Exercises 37–52, perform the indicated operations and write th...

Question

In Exercises 37–52, perform the indicated operations and write the result in standard form.

√-64 - √-25

Accepted Answer

Welcome back. I'm so glad you're here. We've got these two numbers. The square root of negative 81 the square root of negative 16 and we're taking the difference between those two. We're subtracting them and we want to express our answer in standard form. What is standard form? Well when we have got the square root of a negative number, it means we're dealing with complex numbers and the standard form of a complex number is A plus B. I. So we want to get this in terms of I and we recall from previous lessons that by definition I is the square root of negative one. And hey, we've got negatives inside of our square roots and let's see if we can make it look like the square root of negative one. We could rewrite the square root of negative 81 as the square root of negative one, times 81 minus And the square root of negative 16 as the square root of negative one times 16. And we know from the product rule that this is the same thing as the squared of negative one times the square root of minus. The square root of negative one times the square root of 16. And we can replace these square roots of negative one with eyes. So we've got I times the square root of 81 minus I times the square root of 16. And we know that the square root of 81. Well that's nine. So this is nine I minus And we know that the squared of 16. Well that's four. So this is four I. Now these are like terms, we can just subtract nine I minus four. I is five eyes left over. We look at our answer choices in this matches with answer choice B. Well done, we'll catch you on the next one.

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