Find the square root of `1 (56)/(169).`

Answer

To find the square root of the mixed fraction \(1 \frac{56}{169}\), we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
To convert the mixed fraction \(1 \frac{56}{169}\) into an improper fraction, we use the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]
Here, the whole number is 1, the numerator is 56, and the denominator is 169.

Calculating:
\[ 1 \times 169 + 56 = 169 + 56 = 225 \]
So, the improper fraction is:
\[ \frac{225}{169} \]

### Step 2: Write the square root of the improper fraction
Now we need to find the square root of \(\frac{225}{169}\):
\[ \sqrt{\frac{225}{169}} = \frac{\sqrt{225}}{\sqrt{169}} \]

### Step 3: Calculate the square roots of the numerator and denominator
Now we calculate the square roots:
- The square root of 225 is 15 (since \(15 \times 15 = 225\)).
- The square root of 169 is 13 (since \(13 \times 13 = 169\)).

So we have:
\[ \sqrt{225} = 15 \quad \text{and} \quad \sqrt{169} = 13 \]

### Step 4: Write the final answer
Putting it all together, we get:
\[ \sqrt{\frac{225}{169}} = \frac{15}{13} \]

Thus, the square root of \(1 \frac{56}{169}\) is:
\[ \frac{15}{13} \]

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