`sqrt((0.081 xx 0.484)/(0.0064 xx 6.25))` is equal to

Options

A. 9
B. 0.9
C. 99
D. 0.99

Answer

To solve the expression \( \sqrt{\frac{0.081 \times 0.484}{0.0064 \times 6.25}} \), we can follow these steps:

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

### Step 2: Eliminate decimals
To simplify the calculation, we can eliminate the decimals by multiplying the numerator and denominator by appropriate powers of 10.

- The number \(0.081\) has 3 decimal places, so we multiply it by \(1000\).
- The number \(0.484\) has 3 decimal places, so we multiply it by \(1000\).
- The number \(0.0064\) has 4 decimal places, so we multiply it by \(10000\).
- The number \(6.25\) has 2 decimal places, so we multiply it by \(100\).

This gives us:
\[ \sqrt{\frac{81 \times 484 \times 1000 \times 1000}{64 \times 625 \times 10000}} \]

### Step 3: Simplify the expression
Now we can simplify the expression:
\[ \sqrt{\frac{81 \times 484}{64 \times 625}} \]
Since \(1000 \times 1000\) cancels out with \(10000\).

### Step 4: Calculate square roots
Next, we can take the square root of the individual components:
- The square root of \(81\) is \(9\).
- The square root of \(484\) is \(22\).
- The square root of \(64\) is \(8\).
- The square root of \(625\) is \(25\).

Thus, the expression simplifies to:
\[ \sqrt{\frac{9^2 \times 22^2}{8^2 \times 25^2}} = \frac{9 \times 22}{8 \times 25} \]

### Step 5: Calculate the final value
Now we can calculate:
\[ \frac{198}{200} = 0.99 \]

### Final Answer
Therefore, the value of \( \sqrt{\frac{0.081 \times 0.484}{0.0064 \times 6.25}} \) is \(0.99\).

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