Questions: Write 4 √5[12] as an entire radical. Select one: a. √5[12288] b. √5[2304] c. √5[995328] d. √5[192]

Solution Steps

To express \(4 \sqrt[5]{12}\) as an entire radical, we need to incorporate the coefficient 4 into the radical. This can be done by raising 4 to the power of 5 (since the radical is a fifth root) and multiplying it by 12. The result will be the radicand of the new fifth root.

To convert \(4\) into a radical form suitable for combining with \(\sqrt[5]{12}\), we express it as: \[ 4 = \sqrt[5]{4^5} = \sqrt[5]{1024} \]

Now we can combine the two expressions: \[ 4 \sqrt[5]{12} = \sqrt[5]{1024} \cdot \sqrt[5]{12} = \sqrt[5]{1024 \cdot 12} \]

Next, we calculate the product: \[ 1024 \cdot 12 = 12288 \] Thus, we can rewrite the expression as: \[ 4 \sqrt[5]{12} = \sqrt[5]{12288} \]

Final Answer