Problem 69 - Algebra 1: Concepts and Skills

Question

Simplify the radical expression. $$4 \sqrt{\frac{11}{16}}$$

Step-by-Step Solution

Answer

The simplified form of the given radical expression is \(\sqrt{11}\).

Step 1: Identify the Square Roots

Firstly, recognize that both 11 and 16 are under the square root. We can rewrite \(4 \sqrt{\frac{11}{16}}\) as \(4 \frac{\sqrt{11}}{\sqrt{16}}\). The square root of 16 is 4.

Step 2: Simplify the Fraction

Now, simplify the fraction. We replace \(\sqrt{16}\) with its square root, which is 4. Our expression is now \(4 \frac{\sqrt{11}}{4}\). After cancelling out 4 in the numerator and denominator, our expression simplifies to \(\sqrt{11}\).

Step 3: Final Simplification

The expression is now in its simplest form, its square root cannot be simplified any further. Thus, the final simplified radical expression is \(\sqrt{11}\).