If `a^(1/2) + b^(1/2) - c^(1/2)` = 0 then the value of `(a+b-c)^2` is . . . .

Explanation

Here, `a^(1/2)+b^(1/2) -c^(1/2) = 0`

`=>a^(1/2)+b^(1/2) = c^(1/2)`

Squaring both sides,

`=>(a^(1/2))^2+(b^(1/2))^2+2(a^(1/2))(b^(1/2)) = (c^(1/2))^2`

`=>a+b+2sqrt(ab) = c`

`=>a+b-c = -2sqrt(ab)`

Again, squaring both sides,

`(a+b-c)^2 = (-2sqrt(ab)) => (a+b-c)^2 =4ab`