In each of these questions, two equations (I) and (II) are given. Solve the equations and mark the correct option
I. ` x^(2) = 625`
II. ` y = sqrt(625)`

Options

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

Answer

To solve the given equations, let's break down the steps clearly:

### Step 1: Solve the first equation
The first equation is:
\[ x^2 = 625 \]

To solve for \( x \), we take the square root of both sides:
\[ x = \pm \sqrt{625} \]

Calculating the square root:
\[ \sqrt{625} = 25 \]

Thus, the solutions for \( x \) are:
\[ x = 25 \quad \text{and} \quad x = -25 \]

### Step 2: Solve the second equation
The second equation is:
\[ y = \sqrt{625} \]

Calculating the square root:
\[ y = 25 \]

### Step 3: Compare the values of \( x \) and \( y \)
From the solutions we found:
- The possible values for \( x \) are \( 25 \) and \( -25 \).
- The value for \( y \) is \( 25 \).

Now we compare:
1. For \( x = 25 \):
\[ x = y \]

2. For \( x = -25 \):
\[ x < y \]

### Step 4: Combine the results
From our comparisons, we can conclude:
- When \( x = 25 \), \( x \) is equal to \( y \).
- When \( x = -25 \), \( x \) is less than \( y \).

Thus, we can summarize that:
\[ x \leq y \]

### Final Answer
The final relation we derived is:
\[ x \leq y \]