Questions: Simplify the radical: ∛72 A. 8∛36 B. 6∛2 C. 8∛9 D. 2∛9

Solution Steps

To simplify the cube root of 72, we need to find the prime factorization of 72 and then group the factors into sets of three, since we are dealing with a cube root. This will allow us to simplify the expression by taking one factor out of the radical for each complete set of three.

To simplify \( \sqrt[3]{72} \), we first find the prime factorization of 72. The prime factors of 72 are: \[ 72 = 2^3 \times 3^2 \]

Next, we group the factors into sets of three since we are dealing with a cube root. From the factorization:

• \( 2^3 \) contributes \( 2 \) to the outside of the radical.
• \( 3^2 \) remains inside the radical since it does not form a complete set of three.

Thus, we can express the simplified form of \( \sqrt[3]{72} \) as: \[ \sqrt[3]{72} = 2 \cdot \sqrt[3]{9} \]

Final Answer