SOLUTION: Assume that both sqrt(x) and sqrt(y) are simplified completely and that  ≠ . Why is it always possible to multiply sqrt(x)and sqrt(y) together and get sqrt(xy) for the pr

Algebra ->  Test -> SOLUTION: Assume that both sqrt(x) and sqrt(y) are simplified completely and that  ≠ . Why is it always possible to multiply sqrt(x)and sqrt(y) together and get sqrt(xy) for the pr      Log On


   

Question 964707: Assume that both sqrt(x) and sqrt(y) are simplified completely and that  ≠ .
Why is it always possible to multiply sqrt(x)and sqrt(y) together and get sqrt(xy) for the product, but not always possible to add sqrt(x) and sqrt(y) together and get sqrt(x+y)
for the sum?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Because,
sqrt%28x%29%2Asqrt%28y%29=sqrt%28xy%29
but
sqrt%28x%29%2Bsqrt%28y%29%3C%3Esqrt%28x%2By%29
.
.
.
Let's assume it did,
sqrt%28x%29%2Bsqrt%28y%29=sqrt%28x%2By%29
Square both sides,
%28sqrt%28x%29%2Bsqrt%28y%29%29%5E2=x%2By
sqrt%28x%29sqrt%28x%29%2B2sqrt%28x%29sqrt%28y%29%2Bsqrt%28y%29sqrt%28y%29=x%2By
x%2B2sqrt%28xy%29%2By=x%2By
2sqrt%28xy%29=0
The left side is only equal to the right when x=0 or y=0 or x=y=0.
So it's not an identity, so,
sqrt%28x%29%2Bsqrt%28y%29%3C%3Esqrt%28x%2By%29