Chapter 9.1, Problem 12E

To determine

To write: whether the expression $6-\sqrt[3]{54}$ is in simplest form or not.

Answer to Problem 12E

The required answer is: No, $6-\sqrt[3]{54}$ is not in simplest form

Explanation of Solution

Given information:

The given expression: $6-\sqrt[3]{54}$

Calculation:

The expression $6-\sqrt[3]{54}$ is not in simplest form because it can be further simplified:

  $6-\sqrt[3]{54}=6-\sqrt[3]{27\cdot 2}$

(Factors using the greatest perfect cube factor)

  $=6-\sqrt[3]{27}\cdot \sqrt[3]{2}$

(Product property of cube roots)

  $=6-3\sqrt[3]{2}$

(Simplify)