Question

Given that $a\neq b$ is it ever possible to have $\sqrt{a} +\sqrt{b} =\sqrt{a+b}$? Explain.

Answer 1

Answer:

Step-by-step explanation:

√a+√b=√(a+b)

squaring

a+b+2√a√b=a+b

or 2√a√b=0

which is possible only if a=0 or b=0

Both a and b can't be zero as a≠b

Answer 2

Answer:

No, this is not possible because when using squaring you get a+b+2√a√b = a+b or 2√a√b = 0 which is only possible if both a and b are 0. And because a and b can't be the same then √a√b = √a+b is not possible.

Step-by-step explanation: