Each of the following questions is provided with 2 statements i.e. Statement I & Statement II. You have the solve them and mark the correct option
I. ` x^(2) = 256`
II. ` y = sqrt(256)`

Options

A. ` x gt y`
B. ` x lt y `
C. ` x le y `
D. ` x ge y`

Answer

To solve the given statements, we will analyze each statement step by step.

### Step 1: Solve Statement I
The first statement is:
\[ x^2 = 256 \]

To find \( x \), we need to take the square root of both sides. Remember that taking the square root of a squared variable gives two possible values (positive and negative).

\[ x = \pm \sqrt{256} \]

Calculating the square root:
\[ \sqrt{256} = 16 \]

Thus, we have:
\[ x = 16 \quad \text{or} \quad x = -16 \]

### Step 2: Solve Statement II
The second statement is:
\[ y = \sqrt{256} \]

Calculating the square root:
\[ y = 16 \]

### Step 3: Compare the Values of \( x \) and \( y \)
Now we have the values:
- From Statement I: \( x = 16 \) or \( x = -16 \)
- From Statement II: \( y = 16 \)

Now we will compare the values:
1. If \( x = 16 \):
- Then \( x = y \) (since both are 16).

2. If \( x = -16 \):
- Then \( x < y \) (since -16 is less than 16).

### Conclusion
From the analysis, we can conclude that:
- \( x \) can either be equal to \( y \) or less than \( y \).

Thus, the relation can be expressed as:
\[ x \leq y \]

### Final Answer
The correct option is:
**C: \( x \leq y \)**

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