Which of the following is equal to 25?

Options

A. `((0.22)^(2))/(0.2 xx (2.2)^(2))`
B. `((0.022)^(2))/(2.2 xx 0.022)`
C. `((2.2)^(2))/(22^(2) xx (0.02)^(2))`
D. `((0.22)^(2))/(22^(2) xx 0.02)`

Answer

To solve the question "Which of the following is equal to 25?", we will analyze each option step by step.

### Step-by-Step Solution:

**Option 1: 0.22 × 0.22**
1. Calculate \(0.22 \times 0.22\).
- First, convert \(0.22\) into a fraction: \(0.22 = \frac{22}{100}\).
- So, \(0.22 \times 0.22 = \left(\frac{22}{100}\right) \times \left(\frac{22}{100}\right) = \frac{22 \times 22}{100 \times 100} = \frac{484}{10000}\).
2. Convert \(\frac{484}{10000}\) to decimal:
- \(484 \div 10000 = 0.0484\).
3. Since \(0.0484\) is not equal to \(25\), **Option 1 is incorrect**.

**Option 2: 0.022 × 0.022**
1. Calculate \(0.022 \times 0.022\).
- Convert \(0.022\) into a fraction: \(0.022 = \frac{22}{1000}\).
- So, \(0.022 \times 0.022 = \left(\frac{22}{1000}\right) \times \left(\frac{22}{1000}\right) = \frac{22 \times 22}{1000 \times 1000} = \frac{484}{1000000}\).
2. Convert \(\frac{484}{1000000}\) to decimal:
- \(484 \div 1000000 = 0.000484\).
3. Since \(0.000484\) is not equal to \(25\), **Option 2 is incorrect**.

**Option 3: 2.2 × 2.2**
1. Calculate \(2.2 \times 2.2\).
- Convert \(2.2\) into a fraction: \(2.2 = \frac{22}{10}\).
- So, \(2.2 \times 2.2 = \left(\frac{22}{10}\right) \times \left(\frac{22}{10}\right) = \frac{22 \times 22}{10 \times 10} = \frac{484}{100}\).
2. Convert \(\frac{484}{100}\) to decimal:
- \(484 \div 100 = 4.84\).
3. Since \(4.84\) is not equal to \(25\), **Option 3 is incorrect**.

**Option 4: 0.22 × 0.22**
1. Calculate \(0.22 \times 0.22\) again for verification.
- We already calculated this in Option 1 and found it to be \(0.0484\).
2. Since \(0.0484\) is not equal to \(25\), **Option 4 is incorrect**.

### Conclusion:
After evaluating all the options, none of them are equal to \(25\). Therefore, the answer is that none of the provided options are equal to \(25\).