Problem 66 - Algebra 1: Concepts and Skills

Question

Simplify the radical expression. $$\sqrt{\frac{20}{25}}$$

Step-by-Step Solution

Answer

The simplified form of the given radical expression \(\sqrt{\frac{20}{25}}\) is \(2\sqrt{5}/5\).

Step 1: Simplify the Numbers Under the Radical

First, simplify the numbers under the radical. So, you simplify the fraction \(\frac{20}{25}\) which simplifies to \(\frac{4}{5}\). Therefore, the radical expression becomes \(\sqrt{\frac{4}{5}}\).

Step 2: Break Up the Radical

Now, you can take the square root of each number separately. So, the resulting expression becomes \(\sqrt{4}/\sqrt{5}\).

Step 3: Simplify the Square Roots

Now, calculate the square root of each number. The square root of 4 is known to be 2, and the square root of 5 can't be simplified further, therefore, it remains as \(\sqrt{5}\). So the simplified radical expression is \(2/\sqrt{5}\).

Step 4: Rationalize the Denominator

To remove the square root from the denominator, multiply both the numerator and denominator by the square root, so it becomes \(2\sqrt{5}/5\).