Find the square root of :
`96(1)/(25)`

Answer

To find the square root of \( 96 \frac{1}{25} \), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \( 96 \frac{1}{25} \) can be converted to an improper fraction.

\[ 96 \frac{1}{25} = 96 + \frac{1}{25} = \frac{96 \times 25 + 1}{25} = \frac{2400 + 1}{25} = \frac{2401}{25} \]

### Step 2: Find the square root of the improper fraction
Now, we need to find the square root of \( \frac{2401}{25} \).

\[ \sqrt{\frac{2401}{25}} = \frac{\sqrt{2401}}{\sqrt{25}} \]

### Step 3: Calculate the square roots of the numerator and denominator
Next, we calculate the square roots of \( 2401 \) and \( 25 \).

- The square root of \( 25 \) is \( 5 \).
- The square root of \( 2401 \) can be calculated as follows:

\[ 2401 = 49 \times 49 \implies \sqrt{2401} = 49 \]

### Step 4: Combine the results
Now we can combine the results from Step 2 and Step 3.

\[ \sqrt{\frac{2401}{25}} = \frac{49}{5} \]

### Final Answer
Thus, the square root of \( 96 \frac{1}{25} \) is

\[ \frac{49}{5} \]

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