t Use the product rule to simplify the radical. sqrt (567) sqrt (567)=square (Type an exact answer in simplified form.)

To simplify the radical using the product rule, we first need to factorize 567 into its prime factors.1. **Factorize 567:** - 567 is divisible by 3 (since the sum of its digits, 5 + 6 + 7 = 18, is divisible by 3). - - 189 is also divisible by 3. - - 63 is also divisible by 3. - - 21 is also divisible by 3. - So, the prime factorization of 567 is: 2. **Apply the product rule for radicals:** The product rule states that .Using this rule, we can write: 3. **Simplify the expression:** We know that , because the square root of a power of 3 where the exponent is even simplifies directly.Thus, Therefore, the simplified form of is: