The greatest of the following numbers `0.16`, `sqrt(0.16)`, `(0.16)^(2)`, `0.44` is

Options

A. `0.16`
B. `sqrt(0.16)`
C. `0.44`
D. `(0.16)^(2)`

Answer

To find the greatest number among `0.16`, `sqrt(0.16)`, `(0.16)^(2)`, and `0.44`, we will evaluate each expression step by step.

### Step 1: Evaluate `0.16`
The first number is simply `0.16`.

### Step 2: Evaluate `sqrt(0.16)`
To find the square root of `0.16`, we can express it as:
\[ \sqrt{0.16} = \sqrt{\frac{16}{100}} = \sqrt{\frac{4^2}{10^2}} = \frac{4}{10} = 0.4 \]

### Step 3: Evaluate `(0.16)^(2)`
Next, we will calculate `0.16` squared:
\[ (0.16)^2 = 0.16 \times 0.16 = 0.0256 \]

### Step 4: Evaluate `0.44`
The last number is `0.44`, which is already in its simplest form.

### Step 5: Compare all the evaluated numbers
Now we have the following values:
- `0.16`
- `sqrt(0.16) = 0.4`
- `(0.16)^(2) = 0.0256`
- `0.44`

### Step 6: Identify the greatest number
Comparing these values:
- `0.16` is less than `0.4`
- `0.4` is less than `0.44`
- `0.0256` is less than all the others

Thus, the greatest number among them is:
\[ \text{Greatest number} = 0.44 \]

### Final Answer:
The greatest of the following numbers is **0.44**.

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