Tính: √(17-4√(9+√45))

To simplify the expression √(17-4√(9+√45)), we can follow these steps:

1. First, let's simplify the innermost square root, √45.
√45 = √(9 * 5) = √9 * √5 = 3√5

2. Next, let's substitute the simplified value back into the expression.
√(17-4√(9+√45)) = √(17-4√(9+3√5))

3. Now, let's simplify the innermost square root, √(9+3√5).
To simplify this, we need to find two numbers that multiply to give 9 and add up to 3√5.
The numbers are 3 and √5.
Therefore, √(9+3√5) = √9 + √5 = 3 + √5

4. Substitute the simplified value back into the expression.
√(17-4√(9+3√5)) = √(17-4(3+√5))
= √(17-12-4√5)
= √(5-4√5)

5. Finally, let's simplify the innermost square root, √(5-4√5).
To simplify this, we need to find two numbers that multiply to give 5 and add up to 4√5.
The numbers are √5 and √5.
Therefore, √(5-4√5) = √5 - √5 = 0

Therefore, the simplified expression is 0.