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

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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)   (Show Source): You can put this solution on YOUR website!
Because,

but

.
.
.
Let's assume it did,

Square both sides,




The left side is only equal to the right when or or .
So it's not an identity, so,


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