In the following, which is the greatest number?

Options

A. ` [(2+2)^2]^2`
B. `(2+2 + 2)^2`
C. `(4)^2`
D. `(2xx2xx2)^2`

Answer

To determine which of the given options is the greatest number, we will evaluate each option step by step.

### Step-by-Step Solution:

1. **Evaluate Option 1: \( (2 + 2)^2 \) squared**
- First, calculate \( 2 + 2 \):
\[ 2 + 2 = 4 \]
- Next, square the result:
\[ 4^2 = 16 \]
- Finally, square this result again:
\[ 16^2 = 256 \]
- So, Option 1 gives us **256**.

2. **Evaluate Option 2: \( (2 + 2 + 2)^2 \)**
- First, calculate \( 2 + 2 + 2 \):
\[ 2 + 2 + 2 = 6 \]
- Next, square the result:
\[ 6^2 = 36 \]
- So, Option 2 gives us **36**.

3. **Evaluate Option 3: \( 4^2 \)**
- Calculate \( 4^2 \):
\[ 4^2 = 16 \]
- So, Option 3 gives us **16**.

4. **Evaluate Option 4: \( (2 \times 2 \times 2)^2 \)**
- First, calculate \( 2 \times 2 \times 2 \):
\[ 2 \times 2 \times 2 = 8 \]
- Next, square the result:
\[ 8^2 = 64 \]
- So, Option 4 gives us **64**.

5. **Compare All Results:**
- Option 1: 256
- Option 2: 36
- Option 3: 16
- Option 4: 64

6. **Conclusion:**
- The greatest number among the options is **256** from Option 1.

### Final Answer:
The greatest number is **Option 1: 256**.