Simplify the expression. $$ \sqrt{\frac{448}{256}} $$

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UpStudy AI · Accepted Answer

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:**

$$
\frac{\sqrt{7}}{2}
$$
$$\frac{\sqrt{7}}{2}$$

Simplify the expression.

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