# Disprove a statement

• April 7th 2009, 01:45 PM
nikie1o2
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?
• April 7th 2009, 02:12 PM
Reckoner
Quote:

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 $X=Y=1.$
• April 14th 2009, 07:57 PM
rangr
The more algebraic proof would be to square both sides of the equation and show them they are not the same.