How do you simplify √512?

To simplify √512, follow these steps:

Find the prime factorization of 512:

Start by dividing 512 by 2, the smallest prime number.
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
So, the prime factorization of 512 is:
512 = 2^9.

Apply the square root:

Now, use the property of square roots: √(a^b) = a^(b/2).
√512 = √(2^9).
Simplify the square root:

√(2^9) = 2^(9/2) = 2^4 × 2^(1/2) = 16√2.
Thus, the simplified form of √512 is:
16√2.