The largest among the numbers `(0.1)^(2), sqrt(0.0121) , 0.12 and sqrt(0.0004)` is

Options

A. `(0.1)^(2)`
B. `sqrt(0.0121)`
C. `0.12`
D. `sqrt(0.0004)`

Answer

To find the largest among the numbers \( (0.1)^2, \sqrt{0.0121}, 0.12, \) and \( \sqrt{0.0004} \), we will calculate the value of each expression step by step.

### Step 1: Calculate \( (0.1)^2 \)
\[ (0.1)^2 = 0.1 \times 0.1 = 0.01 \]

**Hint:** To square a decimal, multiply the number by itself.

### Step 2: Calculate \( \sqrt{0.0121} \)
We can express \( 0.0121 \) as \( \frac{121}{10000} \):
\[ \sqrt{0.0121} = \sqrt{\frac{121}{10000}} = \frac{\sqrt{121}}{\sqrt{10000}} = \frac{11}{100} = 0.11 \]

**Hint:** When taking the square root of a fraction, take the square root of the numerator and the denominator separately.

### Step 3: Identify the value of \( 0.12 \)
The value is already given as:
\[ 0.12 \]

**Hint:** Sometimes, values are already in their simplest form and do not need further calculation.

### Step 4: Calculate \( \sqrt{0.0004} \)
We can express \( 0.0004 \) as \( \frac{4}{10000} \):
\[ \sqrt{0.0004} = \sqrt{\frac{4}{10000}} = \frac{\sqrt{4}}{\sqrt{10000}} = \frac{2}{100} = 0.02 \]

**Hint:** Similar to the previous step, express the decimal as a fraction to simplify the square root calculation.

### Step 5: Compare all the values
Now we have the values:
- \( (0.1)^2 = 0.01 \)
- \( \sqrt{0.0121} = 0.11 \)
- \( 0.12 = 0.12 \)
- \( \sqrt{0.0004} = 0.02 \)

Now we compare:
- \( 0.01 < 0.02 < 0.11 < 0.12 \)

### Conclusion
The largest number among the four is:
\[ \text{Largest} = 0.12 \]

**Final Answer:** \( 0.12 \)

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