Problem 67 - College Algebra

Question

Simplify the radical expressions if possible. $$\sqrt[3]{32}$$

Step-by-Step Solution

Answer

The simplified form of \(\sqrt[3]{32}\) is \(2\sqrt[3]{4}\)

Step 1: Define the Problem

We need to simplify the expression \(\sqrt[3]{32}\). To do that, we need to find the cube root of 32.

Step 2: Find the Cubes

Remember the cubes. The number 2 cubed is 8, 3 cubed is 27 and 4 cubed is 64. So the largest cube that divides 32 without leaving a remainder is 8 which corresponds to the number 2.

Step 3: Simplify the Expression

So, start by rewriting 32 as 8 times 4, then replace 8 with 2 cubed to get \(\sqrt[3]{2^3*4}\). Applying the cube root results in 2. Thus, the expression simplifies to \(2\sqrt[3]{4}\)