Evaluate:
`sqrt (156.25)`

Answer

To evaluate \( \sqrt{156.25} \), we can follow these steps:

### Step 1: Remove the Decimal
To simplify the calculation, we can remove the decimal by rewriting \( 156.25 \) as a fraction. We can express it as:
\[ 156.25 = \frac{15625}{100} \]
This means we need to find:
\[ \sqrt{156.25} = \sqrt{\frac{15625}{100}} = \frac{\sqrt{15625}}{\sqrt{100}} \]

### Step 2: Calculate the Square Root of the Denominator
We know that:
\[ \sqrt{100} = 10 \]

### Step 3: Calculate the Square Root of the Numerator
Now, we need to find \( \sqrt{15625} \). We can do this by prime factorization or by recognizing that \( 15625 \) is a perfect square.

To factor \( 15625 \):
- Divide by \( 5 \):
- \( 15625 \div 5 = 3125 \)
- \( 3125 \div 5 = 625 \)
- \( 625 \div 5 = 125 \)
- \( 125 \div 5 = 25 \)
- \( 25 \div 5 = 5 \)
- \( 5 \div 5 = 1 \)

Thus, \( 15625 = 5^6 \).

Now, we can find the square root:
\[ \sqrt{15625} = \sqrt{5^6} = 5^{6/2} = 5^3 = 125 \]

### Step 4: Combine the Results
Now, we can substitute back into our equation:
\[ \sqrt{156.25} = \frac{\sqrt{15625}}{\sqrt{100}} = \frac{125}{10} = 12.5 \]

### Final Answer
Thus, the value of \( \sqrt{156.25} \) is:
\[ \boxed{12.5} \]

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