`((0.081xx0.484)/(0.0064xx6.25))^(1/2)=?`

Options

A. 2.3
B. 1.5
C. 0.99
D. 3.6

Explanation

To solve the expression \(\left(\frac{0.081 \times 0.484}{0.0064 \times 6.25}\right)^{\frac{1}{2}}\), we can follow these steps:

### Step 1: Simplify the expression inside the parentheses
We start with the expression:
\[ \frac{0.081 \times 0.484}{0.0064 \times 6.25} \]

### Step 2: Convert decimals to fractions
To make calculations easier, we can convert the decimals to fractions:
- \(0.081 = \frac{81}{1000}\)
- \(0.484 = \frac{484}{1000}\)
- \(0.0064 = \frac{64}{10000}\)
- \(6.25 = \frac{625}{100}\)

Now, substituting these values into the expression gives us:
\[ \frac{\frac{81}{1000} \times \frac{484}{1000}}{\frac{64}{10000} \times \frac{625}{100}} \]

### Step 3: Multiply the fractions
Now, we can multiply the fractions in the numerator and denominator:
- Numerator:
\[ 81 \times 484 = 39264 \]
- Denominator:
\[ 64 \times 625 = 40000 \]

Thus, the expression simplifies to:
\[ \frac{39264}{40000} \]

### Step 4: Simplify the fraction
Next, we can simplify the fraction \(\frac{39264}{40000}\). We can divide both the numerator and the denominator by 64:
\[ \frac{39264 \div 64}{40000 \div 64} = \frac{613}{625} \]

### Step 5: Take the square root
Now we need to take the square root of the simplified fraction:
\[ \left(\frac{613}{625}\right)^{\frac{1}{2}} = \frac{\sqrt{613}}{\sqrt{625}} = \frac{\sqrt{613}}{25} \]

### Step 6: Approximate the square root
To find \(\sqrt{613}\), we can approximate it. Since \(24^2 = 576\) and \(25^2 = 625\), we know that:
\[ \sqrt{613} \approx 24.8 \]
Thus,
\[ \frac{\sqrt{613}}{25} \approx \frac{24.8}{25} \approx 0.992 \]

### Final Answer
Therefore, the final answer is approximately:
\[ 0.992 \]