The square root of `21 (51)/(169)` is

Options

A. `5 (8)/(13)`
B. `4 (8)/(13)`
C. `4 (3)/(13)`
D. `5 (5)/(13)`

Answer

To solve the problem of finding the square root of \( 21 \frac{51}{169} \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
First, we need to convert the mixed number \( 21 \frac{51}{169} \) into an improper fraction.

\[ 21 \frac{51}{169} = \frac{21 \times 169 + 51}{169} = \frac{3559 + 51}{169} = \frac{3600}{169} \]

### Step 2: Find the square root of the fraction
Now, we can find the square root of the fraction \( \frac{3600}{169} \).

\[ \sqrt{\frac{3600}{169}} = \frac{\sqrt{3600}}{\sqrt{169}} \]

### Step 3: Calculate the square roots
Next, we calculate the square roots of the numerator and the denominator.

\[ \sqrt{3600} = 60 \quad \text{and} \quad \sqrt{169} = 13 \]

### Step 4: Form the fraction
Now we can form the fraction from the square roots we calculated.

\[ \frac{\sqrt{3600}}{\sqrt{169}} = \frac{60}{13} \]

### Step 5: Simplify if necessary
The fraction \( \frac{60}{13} \) is already in its simplest form.

### Final Answer
Thus, the square root of \( 21 \frac{51}{169} \) is:

\[ \frac{60}{13} \]

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