Box Lengths

[jbigs]

Here is the problem

If the box pictured to the right is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?

I am having a problem solving the following equation: BC = ( x^2 + x(2^1/2))^1/2=x*3^1/2

I can not figure out this equation and how it equals x times the square root of 3...

Any help would be appreciated!

John

[StaceyKoprince]

Please remember to follow protocol:
1) your subject should be the first 5-8 words in the question
2) post the FULL text of the question including answer choices

Please review the sticky with instructions for posting multiple choice questions.

Also, I think you forgot to load the image - I don't see a box! If you don't know how to load images, please just tell us the title of the problem (as it shows up in your problem list). (I think you used that as your subject header here - again, review the sticky for protocol.)

Here's the equation as typed properly (the version above is missing a square):

BC = [x^2 + (x*SQRT2)^2]^1/2=x*SQRT3

let's start with (x*SQRT2)^2
square each item in the parentheses to get x^2 * 2 which equals 2x^2
I now have:
[x^2 + 2x^2]^1/2
[3x^2]^1/2
if I square root what's in the parentheses, x^2 simply becomes x, and 3 becomes SQRT3.