Question

Simplify the cube root of 147m, then multiply the answer by 3m². Provide the simplified radical and the final answer.

a. 7m * cube root of (3m)
b. 21m³ * cube root of (m)
c. 7m³ * cube root of (3)
d. 21m * cube root of (m)

Answer 1

To simplify the cube root of 147m, factorize the number 147 and simplify it as the cube root of 3 * 7 * 7 * m, which is 7 * cube root of (3). Then multiply this answer by 3m².

Step-by-step explanation:

To simplify the cube root of 147m, we need to factorize the number 147. The prime factorization of 147 is 3 * 7 * 7. We can simplify it as the cube root of 3 * 7 * 7 * m. The cube root of 3 * 7 * 7 is 7 * cube root of (3).

Next, we need to multiply this answer by 3m². So, the final answer is 7m * cube root of (3) * 3m².