# Math Help - Disprove a statement

1. ## Disprove a statement

Hey everyone,
Im being asked to disprove: If X and Y are positive real numbers, then the SqRt( X+Y) = SqRt(X) + SqRt(Y). As a counterexample, would letting x= 25 and Y=9 be acceptable? Since SqRt(x+y) would equal SqRt(34) and SqRt(X) + SqRt(Y)= 5+3=8 and there not equal?

2. Originally Posted by nikie1o2
Hey everyone,
Im being asked to disprove: If X and Y are positive real numbers, then the SqRt( X+Y) = SqRt(X) + SqRt(Y). As a counterexample, would letting x= 25 and Y=9 be acceptable? Since SqRt(x+y) would equal SqRt(34) and SqRt(X) + SqRt(Y)= 5+3=8 and there not equal?
Yes, this will work.

If you want an even simpler counterexample, consider $X=Y=1.$

3. The more algebraic proof would be to square both sides of the equation and show them they are not the same.