# Solving a proof

• Mar 4th 2007, 08:00 AM
sergeantjoker
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.

• Mar 4th 2007, 08:49 AM
Soroban
Hello, sergeantjoker!

Quote:

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.

• Mar 4th 2007, 08:53 AM
sergeantjoker
Thanks alot. Man, do I feel stupid now. I have been working on this problem for 2 days. Thanks again.