more concerned with how the answers are derived?

Question

1. 4 sqrt(2x-1) = 2 was told square both sides which then gets 2x-1^4=2^4 which eventually becomes 2x=17 so X=8.5. Why didn't the 2X get a "^4" added to it?

2. sqrt (-12) = 2i sqrt 3 - what happened to the negative?

Answer 1

You are doing #1 wrong. Square both sides, 16(2x-1) = 4, so 2x-1=1/4

Add 1 to both sides 2x=5/4. Multiply by 1/2, x=5/8

1. sqrt 2x-1 is the same as (2x-1)^1/2

Power to a power means you multiply the exponent ONLY

1/2 x 2 equals 1. Nothing inside the sqrt gets touched.

2. Negative square roots are i's. Thats the definition of i = sqrt (-1)

Answer 2

OK

First one -- The 4 at the beginning of the equation tells me you are mutiplying the sqrt of 2x-1 *4. If that is true, 8.5 is an impossible answer, since 8.5 time 2 -1 would equal 16 and the square root of that is 4 - and when you multiply that by 4 it is WAY more that 2.

Here is what I get
4 sqrt(2x-1) = 2; square both sides
sqrt(2x-1) = 1/2
2x-1 = 1/4
2x = 5/4
x = 5/8

Let's check
4sqrt(2(5/8)-1) = 2 ??
4 sqrt(5/4 -1) = 2 ??
4 sqrt(1/4) = 2??
4 (1/2) = 2 ??
2 = 2 YES!

===============
Sqrt (-12) = Sqrt (-1)(4)(3) = 2i sqrt(3)

The sqrt of -1 by definition is i.

Hope that helps.

Answer 3

okay, first, is it 4 ON THE SQUARE ROOT of (2x-1) = 2? Because I'm confused as to what is aquare rooted. If it is 4 on the sq.root then you would first divide the four on each side which gets you the sqrt of (2x-1)=(1/2). Then you would square each side and you would get 2x-1=1/4. Then you would subtract 1 and divide by 2 to get 3/8.

If you mean the fourth square root then you would first ^4 everything, which isn't called squaring but I don't really know what its called....which would give you 2x-1=16. Then you would eventually get 8.5 like you said. Okay, to answer your question, the 1 didn't get "square" rooted either. If you have the square root of the 9 then you square it, you're left with 9 because whats the square root of 9? Its X^2 = 9 X being the suare root, when you square it you're just multiplying times itself which would give you 9.



Make sense?

Answer 4

4 sqrt(2x-1) = 2
sqrt(2x-1) = 1/2

(2x-1) = 1/4
2x = 5/4
x = 5/8


sqrt (-12) = 2i sqrt 3

sqrt(-1) = i

i sqrt(12) = i * sqrt(4)*sqrt(3)
2i*sqrt(3)

Answer 5

Second one:

sqrt(-12) = sqrt(-1) * sqrt(12)
= sqrt(-1) * sqrt(3 * 4)
= sqrt(-1) * sqrt(3) * sqrt(4)
= 2 * i * sqrt(3)

QED