Question

given that a is inequal to b, is it ever possible to have square root of a + square root of b = square root a+b

Answer 1

Yes, but only if a=0 or b=0

Explanation:

`(a+b)^2=a^2+b^2\\\\a^2+2ab+b^2=a^2+b^2\\\\2ab=0\quad\iff\quad a=0\ \ or\ \ b=0`

Answer 2

Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands. If either a or b equals zero, then the sums would be the same. Since the square root of 0 is 0, adding it to a given radical. Also, adding zero to the radicand would not change the value

Explanation: