Problem 76 - Algebra 1: Concepts and Skills

Question

Simplify the radical expression. $$ \frac{1}{8} \sqrt{32} $$

Step-by-Step Solution

Answer

The simplified form of the given expression \( \frac{1}{8} \sqrt{32} \) is \( \frac{1}{2}\sqrt{2} \).

Step 1: Determine the square root

Start off by finding the square root of 32, which is \( \sqrt{32} = 4\sqrt{2} \). This is because 32 can be written as \(16 * 2\), and the square root of 16 is 4. So we can split the square root as \( \sqrt{16} * \sqrt{2} = 4\sqrt{2} \).

Step 2: Simplify the expression

Next, substitute the simplified square root back into the original expression, to obtain \( \frac{1}{8} * 4\sqrt{2} \).

Step 3: Solve the expression

Multiply \( \frac{1}{8} \) with \(4\sqrt{2}\) to get \( \frac{1}{2}\sqrt{2} \). Here the 4 and 8 simplify to 1 / 2 when multiplied.