In Exercises 29–36, simplify and write the result in standard for...

Question

In Exercises 29–36, simplify and write the result in standard form.√-108

Accepted Answer

welcome back, I'm so glad you're here, we've got this number, the square root of negative 98 we are to express the answer in standard form, so negative the square root of negative 98. Well how could we break that up? That's the same thing as negative one times 98. And now we can take a look at 98, we can make a factor tree, we know that's divisible by two. What happens to be two times 49 and we know that 49 is seven times seven. So inside that square root we've got the square root of negative one times seven times seven. That's seven squared times two. And then we take a look at the index here and there's that unwritten to here. And I think of them like the gatekeeper and he says there have to be two of you in order for you to come out. And the seven gets really excited that the seven, like the sevens are like there's two of us, we can come out and the gatekeeper says yes you may, you can come out because there's two of you. So the seven comes outside the square root bracket and now there's just the negative one and the two inside and the two is like so happy to have company but the negative one goes ha ha! Did you know people have been imagining about me and they decided that the square root of negative one is I the imaginary number and therefore I get to go past this gatekeeper and I get to come out and now it's seven I. On the outside, we get that square root of negative one comes out and that is I. And on the inside is this poor, sad lonely squirt of two. And we look at our answer choices and that matches with answer choice B. Well done, we'll catch you on the next one.

In Exercises 29–36, simplify and write the result in standard form.√-108

Key Concepts

Complex Numbers

Square Roots of Negative Numbers

Standard Form of Complex Numbers

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