Evaluate the following :
`sqrt((1156)/(529))`

Answer

To evaluate the expression \( \sqrt{\frac{1156}{529}} \), we can follow these steps:

### Step 1: Simplify the fraction inside the square root
We start with the expression:
\[ \sqrt{\frac{1156}{529}} \]

### Step 2: Find the square root of the numerator and denominator separately
Next, we can find the square roots of the numerator and the denominator:
\[ \sqrt{1156} \quad \text{and} \quad \sqrt{529} \]

### Step 3: Calculate \( \sqrt{1156} \)
To find \( \sqrt{1156} \), we can factor 1156:
- 1156 can be divided by 2: \( 1156 \div 2 = 578 \)
- 578 can be divided by 2: \( 578 \div 2 = 289 \)
- 289 is \( 17 \times 17 \) (or \( 17^2 \))

Thus, we can express 1156 as:
\[ 1156 = 2^2 \times 17^2 \]
So,
\[ \sqrt{1156} = \sqrt{2^2 \times 17^2} = 2 \times 17 = 34 \]

### Step 4: Calculate \( \sqrt{529} \)
Now, we find \( \sqrt{529} \):
- 529 is \( 23 \times 23 \) (or \( 23^2 \))

Thus, we can express 529 as:
\[ 529 = 23^2 \]
So,
\[ \sqrt{529} = 23 \]

### Step 5: Substitute back into the square root expression
Now we can substitute back into our original expression:
\[ \sqrt{\frac{1156}{529}} = \frac{\sqrt{1156}}{\sqrt{529}} = \frac{34}{23} \]

### Final Answer
Thus, the final result is:
\[ \sqrt{\frac{1156}{529}} = \frac{34}{23} \]

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