Thread: 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?

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

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