Write each number as the product of a real number and i. -√-18...

Question

Write each number as the product of a real number and i. -√-18

Accepted Answer

Hello everyone. We are going to rewrite the expression negative square root of negative 882. Using real numbers. And I so I'm gonna rewrite it myself. The Negative Square Root -882. First thing I recall is that if I can get the negative one out of there and take the square root of it, it will simplify what's under the radical. So my negative sign on the outside stays put and I'm going to split this into the square root of negative one Times The Square Root of 882. I know that the square to negative one is I So now I have negative I Times The Square Root of 882. I recall that if I want to simplify this, I need to find a perfect square that goes evenly into 882. Now 441 will do it. It is a perfect square. But chances are you don't know that perfect square off the top of your head and you likely check one that is more familiar to you. So I'm going to do it actually with the square to 49 times a squared of 18. 1st. The reason being I know the square to 49 is seven and it makes my number a lot smaller, a lot easier to deal with. So I have now negative I times seven Times and I'm Gonna break up the squared of 18. So again, I could find another perfect square that goes in there which would be nine Times the square to two square 29 is three. So I have negative I times seven times three Times The Square to two. When I multiply all the real number of parts together, I get negative 21 I Times The Square to two. That is my solution. So negative 21 i times the square to two. If you didn't see that as your perfect square right off the bat, it'll take you a couple more steps, but you'll get there. This is answer choice. C. Have a good day.

Write each number as the product of a real number and i. -√-18

Key Concepts

Imaginary Unit (i)

Simplifying Square Roots of Negative Numbers

Prime Factorization and Simplification of Radicals

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