This statement is false.
In an isosceles triangle, two sides are of equal length, let’s denote the length of these sides as ‘a’, and the base (the third side) as ‘b’. The statement claims that:
√a + √a = √b
However, if we simplify that, we would get:
2√a = √b
Squaring both sides results in:
4a = b
For this to hold, the length of the base would always have to be four times the length of the equal sides, which is not true for all isosceles triangles. For instance, consider an isosceles triangle with sides of length 3 and base of length 4. Here, √3 + √3 ≠ √4.
Thus, the sum of the square roots of any two sides of an isosceles triangle does not equal the square root of the remaining side in general, proving the statement false.