Problem 75 - Algebra 1: Concepts and Skills

Question

Simplify the radical expression. $$ \frac{1}{3} \sqrt{27} $$

Step-by-Step Solution

Answer

The simplified form of the radical expression \(\frac{1}{3} \sqrt{27}\) is \(\sqrt{3}\)

Step 1: Identify the perfect square factor of the radicand

In the expression, the radicand (27) can be written as a multiple of a perfect square. The highest perfect square that divides 27 evenly is 9. Therefore, \(\sqrt{27}\) can be written as \(\sqrt{9*3}\)

Step 2: Simplify the square root

Since \(9\) is a perfect square, we can take its square root out of the radical. So, \(\sqrt{9*3}\) simplifies to \(3\sqrt{3}\)

Step 3: Multiply the simplified radical by the coefficient

Finally, the coefficient outside the radical (\(1/3\)) multiplies with \(3\sqrt{3}\) which simplifies to \(\sqrt{3}\)