a>b>0

[shibal]

how can i do this w/out plugging in?

a>b>0, then (a^2-b^2)^1/2

oa [spoiler](a+b)^1/2*(a-b)^1/2[/spoiler]

[VP_Jim]

This is a common thing to see on the GMAT. You need to know that:

(a^2-b^2) = (a+b)(a-b)

So, in this problem, you're taking the original expression to the 1/2 power. You can convert into the second expression, and "distribute" that 1/2 to both terms to get:

(a+b)^1/2 x (a-b)^1/2

It's MUCH easier to do this without typing (i.e., on a blackboard) - I hope that makes sense!

[kishore99]

Small correction to previous post,

CORRECT: (a^2 - b^2) = (a+b)(a-b)

WRONG: (a-b)^2 = (a+b)(a-b)

[VP_Jim]

Whoops, sorry. Like I said, much easier to do this with a blackboard. I never have gotten used to using the ^ character for exponents. It makes my brain freeze up. I edited my previous post for clarity's sake.