Help on this one with expression of i?

Question

Okay this is the question : 8 sqrt -3/8

So is this the answer? 8 sqrt -i/4 than I multiply?

8 * i/4 ?

So is the answer 2i ?

Please help. Thanks.

Answer 1

First, there's something very important to remember:

√(xy) = √x * √y

Now, let's apply this to your problem:

√(-3/8) = √(3/8) * √(-1)

Now, let's change your expression according to this:

8 * √(-3/8) = 8 * √(3/8) * √(-1)

Remember that the √(-1) = i, and rewrite the expression:

8 * √(3/8) * i

Now, let's simplify the fraction in the radical:

√(3/8) = √(6/16) = √6/4

Substitute this into the expression:

*** 2i√(6)

Answer 2

i = sqrt of -1

8(sqrt -3/8) = 8 (sqrt (-1 x 3/8))

= 8i (sqrt 3/8) = 8i (sqrt 1/4 x sqrt 3/2)

= 4i (sqrt 3/2) = 4i (sqrt 1/4 x sqrt 6)
= 2i (sqrt 6)

Answer 3

8sqrt(-3/8)
= 8sqrt(3/8)*sqrt(-1)
= 8 sqrt(6/16)i
= 8 sqrt(6)sqrt(1/16)i
= 2isqrt(6)

Answer 4

8 sqrt(-3/8) = sqrt(64) * sqrt(-3/8) = sqrt(-3 * 64 / 8) = sqrt(-24) I hope you can finish from here.