Given, √(ab) is an irrational number.

Let us suppose that √a + √b is a rational number.

So, we can write √a + √b as

√a + √b = p/q .........1 where q ≠ 0

Now, squaring on both side, we get

      (√a + √b)² = (p/q)²

=> a + b + 2*√a * √b = p² /q²

=> a + b + 2*√(ab) = p² /q²

=> 2*√(ab) = p² /q² - (a + b)  ............2

Since, √a + √b are rational, So a and b are also rational.

So, RHS of equation 2 is a rational number.

But it is given that √(ab) is an irrational number.

So, LHS of equation 2 is an irrational number.

which contradict our assumption.

So, it is clear that √a + √b is an irrational number.