Thread: Solving a proof

The problem is:

There are real numbers a and b such that

squareroot(a+b) = squareroot(a) + squareroot(b).

Basically, I have to find two numbers that when added together the resulting squareroot is equal to if I took the square root of each number individually and added them together. I have been trying to figure this out for hours. Teacher basically said that we just have to go through all the numbers to prove it.

Please help!!!

Hello, sergeantjoker!

Find real numbers a and b such that
. . . _____ . . . ._ . . ._
. . √a + b .= .√a + √b

. . . . . . . . . . . . . . . . _____ . . . . . . _ . . . _
Square both sides: . (√a + b)² . = . (√a + √b)²

. . . . . . . . . . . . . . . . . . . . . . . .__
And we have: . a + b . = . a + 2√ab + b

. . . . . . . .__ . . . . . . . . .__
Then: . 2√ab .= .0 . → . √ab .= .0 . → . ab .= .0


Therefore: .either a = 0 or b = 0.

Thanks alot. Man, do I feel stupid now. I have been working on this problem for 2 days. Thanks again.