Simplify the expression. \[ \sqrt{\frac{448}{256}} \]

To simplify the expression \(\sqrt{\frac{448}{256}}\), follow these steps: 1. **Simplify the Fraction Inside the Square Root:** \[ \frac{448}{256} \] - **Find the Greatest Common Divisor (GCD) of 448 and 256:** - The GCD of 448 and 256 is 64. - **Divide both numerator and denominator by the GCD:** \[ \frac{448 \div 64}{256 \div 64} = \frac{7}{4} \] So, the expression becomes: \[ \sqrt{\frac{7}{4}} \] 2. **Simplify the Square Root of a Fraction:** \[ \sqrt{\frac{7}{4}} = \frac{\sqrt{7}}{\sqrt{4}} = \frac{\sqrt{7}}{2} \] Since \(\sqrt{4} = 2\), the expression simplifies to \(\frac{\sqrt{7}}{2}\). **Final Answer:** \[ \frac{\sqrt{7}}{2} \]