Evaluate:
`sqrt (33.64)`

Options

A. `6.8`
B. `5.8`
C. `7.8`
D. `8.8`

Answer

To evaluate \( \sqrt{33.64} \), we can follow these steps:

### Step 1: Remove the Decimal
First, we can express \( 33.64 \) as a fraction to make it easier to work with:
\[ 33.64 = \frac{3364}{100} \]

### Step 2: Apply the Square Root to the Fraction
Now, we can take the square root of both the numerator and the denominator:
\[ \sqrt{33.64} = \sqrt{\frac{3364}{100}} = \frac{\sqrt{3364}}{\sqrt{100}} \]

### Step 3: Calculate the Square Root of the Denominator
The square root of \( 100 \) is:
\[ \sqrt{100} = 10 \]

### Step 4: Calculate the Square Root of the Numerator
Next, we need to find \( \sqrt{3364} \). We can do this by factoring or using long division. For simplicity, let's check for perfect squares:
- \( 58 \times 58 = 3364 \)

Thus, we have:
\[ \sqrt{3364} = 58 \]

### Step 5: Combine the Results
Now we can combine the results from steps 3 and 4:
\[ \sqrt{33.64} = \frac{58}{10} = 5.8 \]

### Final Answer
Therefore, the value of \( \sqrt{33.64} \) is:
\[ \sqrt{33.64} = 5.8 \]

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