Perform the indicated operations and write the result in stand...

Question

Perform the indicated operations and write the result in standard form. √−32 − √−18

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the expression, the square root of negative 700 minus the square root of negative 567 and express our answer in standard form. If necessary for our answer choices, A is negative square root of seven IB is a spirit of seven IC is 10 minus the square of seven I and D is a spirit of 10 minus seven I. So essentially, we just need to write it in standard form. That means write it the way that a complex number would typically be written and we want to simplify it. So it means we want to break down our expression here, the square root of negative 700 minus the square of negative 567 into a simpler form. And you can see that in our answer choices, all of our answer choices are, are either single or double digit. So if we're going to simplify first, we need to see if there is anything both these terms have in common. Well, if you notice both of them have seven as a factor, so we can rewrite it as the square root of negative seven multiplied by the square root of 100 minus the square root of negative seven multiplied by the square root of 81. No, we can factor out the square root of negative seven which will leave us inside the bracket. A skirt of 100 multiplied sorry, subtracting the square root of 81. Now the square of 100 and the script of 81 are some pretty nice numbers because both of them are squared numbers. So we can rewrite it as a script of 100 being and the square of 81 being nine, 10 minus nine is one. So now we're down to the square root of negative seven. We're not done yet because we need to write it in standard form. We need to show that it's a complex number. And remember that for complex numbers, if I rewrite this as the spirit of seven multiplied by the spirit of negative one, the definition of I is the spirit of negative one. So my final answer would just be the square root of seven I which would have been answer choice B thanks for watching everyone. I hope this video helped.

Perform the indicated operations and write the result in standard form. √−32 − √−18

Key Concepts

Imaginary Numbers and Complex Numbers

Simplifying Square Roots

Operations with Complex Numbers

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