Use the product rule to simplify the radical. sqrt (756) sqrt (756)= square (Type an exact answer in simplified form.)

Question

Answer 1

To simplify the radical

using the product rule, we first need to factor 756 into its prime factors.1. **Factor 756:** - 756 is even, so divide by 2:

- 378 is even, so divide by 2 again:

- 189 is divisible by 3 (since the sum of its digits, 18, is divisible by 3):

- 63 is also divisible by 3:

- 21 is divisible by 3:

- Finally, 7 is a prime number.So, the prime factorization of 756 is:

2. **Apply the Product Rule for Radicals:**The product rule states that

. We can apply this rule to separate the perfect squares from the non-perfect squares:

Separate the perfect squares:

Simplify the square roots of the perfect squares:

Calculate the square roots:

Thus, the simplified form of

is:

Therefore, the exact answer in simplified form is:

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