Question

MEDAL AND FAN!
Simplify Square Root of -48 .
A) -4 square root of 3
B) 4 square root of negative 3
C) 4i square root of 3
D) 4 square root of 3 i

Answer 1

@mathmate could you please help me?

Answer 2

I don't think it is A or B since we are learning about i

Answer 3

I know this

Answer 4

It's A
You can't have a negative

Answer 5

no negatives under a square root

Answer 6

c and d do not have negatives

Answer 7

Hints:
1. The square-root of a negative numerical quantity has an "i" attached to it, as you suggest, but for a different reason.
By definition, y=sqrt(x) means y^2=x.
Since i^2=-1, so y^2 becomes negative if y contains i as a factor.
Example: \((4i)^2 = 4^2 i^2 =16(-1)=-16\) (note brackets around 4i.

2. when simplifying sqrt(x) when x is composite (i.e. consists of numerous factors), the work can be simplified by first factoring x.
For example, \(\sqrt{96}=\sqrt{2^5*3}=\sqrt{2^4*2*3}=\sqrt{2^4}*\sqrt{2*3}=2^2\sqrt{6}=4\sqrt 6\)

With the two hints understood, you will have no problem solving the posted problem.

Answer 8

So I am supposed to square and multiply then simplify okie ^_^

Answer 9

oh i'm sorry I didn't pay attention to the answers

Answer 10

If you combine the two hints, you would get
\(\sqrt{-96}=4\sqrt 6 i\)
Check:
\((4\sqrt 6 i)^2 =4^2(\sqrt 6)^2i^2=16(6)(-1)=-96, so that's correct!\)