Simplify and write the result in standard form. √-108

Question

Accepted Answer

welcome back, I'm so glad you're here, We've got this number here, the square root of negative 81 we are to simplify and express that in standard form. Okay, well inside the square root it's negative 81 we can rewrite that as the square root of negative one times 81 in 81. We remember how to work with that. We can build a factor tree 81 is nine times nine and there you go, nine times nine is nine squared. So we can rewrite this as the square root of negative one times nine squared. And now we look at this index here and there's that unwritten unspoken to and I think of him like the gatekeeper and he says in order for you to come out, there have to be two of you, factor and the nines get really excited to go. There's two of us were nine square, there's two of us and the gatekeeper says, yep, you may come out, there are two of you and the nine is so excited to get out. That gets past the gatekeeper. Now there's just 19 on the outside. And we've got nine times the square root of negative one. And he's kind of going ha ha ha ha you didn't get to come out. But the negative one inside that square root goes ha ha I bet you didn't know people have been imagining about me and they have decided that the square root of negative one equals I the imaginary number and I get past the gatekeeper with my imagination and I come outside of that square root bracket and now I am nine I and then I'm kind of size and goes, okay fine, you can come out and that's it, nine. I we look at our answer choices and it's answer choice C Well done, we'll catch you on the next one.

Simplify and write the result in standard form. √-108

Key Concepts

Complex Numbers

Square Roots of Negative Numbers

Standard Form of Complex Numbers

Watch next