Let's simplify the expression:

√(21+4√17) + √(21-4√17)

We can see that the two terms inside the square roots are conjugates of each other, which means their sum will eliminate the radical.

Let's denote x = √(21+4√17) and y = √(21-4√17)

Now we can rewrite the expression as:

x + y

Now let's add x and y:

x + y = √(21 + 4√17) + √(21 - 4√17)
= √(21 + 4√17) + √(21 + 4√17) (since y = √(21 - 4√17) is the conjugate of x)
= 2√(21 + 4√17)

Therefore, the simplified expression is 2√(21 + 4√17).