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

Question

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

(3√(−5) )( −4√(−12) )

Accepted Answer

Hello, everyone. We are asked to simplify the following expression and express the answers in standard form. If necessary, we are given two radical negative seven multiplied by negative eight radical negative 18. Our answer choices are a negative 14 radical 48 B 14 radical C negative 48 radical 14 D 48 radical 14. First, I'm gonna rewrite these because I like to see things in my own handwriting to start with. So I have two radical negative seven and it's being multiplied by negative eight radical negative 18. So I think I'm gonna simplify this one term at a time starting with our first term two radical negative seven. I recall that I can break radical negative seven into radical negative one multiplied by radical seven. And when I do so the square of negative one is I, so I'm gonna bring down the square to seven and bring down the two. And I'm gonna rewrite this expression as two I radical seven. Next looking at negative eight radical negative 18, I wanna see if I can simplify this radical. So within there I know I have the square root of negative one but I also have the squared of two multiplied by the squared of nine. So I look for perfect squares that I can use to simplify. I'm bringing down the negative eight. The squared of negative one is I, the square of two will remain the squared of two and the squared of nine is three. So multiplying all these things together, I have negative eight which will be multiplied by three to give me negative 24 I multiplied by radical two. Now that I've simplified this, I could try to multiply a little bit more. So multiplying our coefficients two multiplied by negative is negative 48. I multiplied by I is I squared and radical seven multiplied by radical two is radical 14. I recall that I squared is the same as negative one. So I'm gonna simplify this one more time. So I have negative 48 multiplied by negative one, then multiplied by the square to 14. Negative 48 multiplied by negative one, gives us a positive 48 multiplied by radical 14. And that is our answer because there is nothing else I can simplify under the radical or in front of it. So that's answer choice. D 48 multiplied by the square of 14 have a nice day.

In Exercises 37–52, perform the indicated operations and write the result in standard form.
(3√(−5) )( −4√(−12) )

Key Concepts

Complex Numbers and Standard Form

Multiplication of Complex Numbers

Simplifying Square Roots of Negative Numbers

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