How do you simplify √468?

To simplify √468, we first find its prime factorization.

Start with 468.
468 is even, so divide by 2:
468 ÷ 2 = 234.
234 is even, so divide by 2 again:
234 ÷ 2 = 117.
117 is divisible by 3 (since the sum of the digits, 1 + 1 + 7 = 9, is divisible by 3):
117 ÷ 3 = 39.
39 is also divisible by 3 (since 3 + 9 = 12, which is divisible by 3):
39 ÷ 3 = 13.
13 is a prime number.
So, the prime factorization of 468 is:
468 = 2 × 2 × 3 × 3 × 13.

Now, simplify √468.
√468 = √(2 × 2 × 3 × 3 × 13).

Group the perfect squares (2 × 2 and 3 × 3): √468 = √(4 × 9 × 13).

Take the square root of the perfect squares (√4 = 2 and √9 = 3): √468 = 2 × 3 × √13.

Simplify the expression: √468 = 6√13.

So, the simplified form of √468 is 6√13.