In each of these questions, two equations I. and II. are given . you have to solve both the equations and answer the following questions
I. ` x^(3) = 2744`
II. ` y^(2) = 324`

Options

A. x = y or no relation
B. ` x lt y`
C. ` x le y `
D. ` x gt y `

Answer

To solve the given equations, we will follow these steps:

### Step 1: Solve the first equation \( x^3 = 2744 \)

To find the value of \( x \), we need to take the cube root of both sides of the equation.

\[ x = \sqrt[3]{2744} \]

### Step 2: Calculate the cube root of 2744

We can recognize that \( 2744 \) is a perfect cube. To find the cube root, we can either factor \( 2744 \) or use a calculator.

Upon factoring, we find:

\[ 2744 = 14^3 \]

Thus,

\[ x = 14 \]

### Step 3: Solve the second equation \( y^2 = 324 \)

To find the value of \( y \), we need to take the square root of both sides of the equation.

\[ y = \sqrt{324} \]

### Step 4: Calculate the square root of 324

The square root of \( 324 \) can be calculated as follows:

\[ y = \pm 18 \]

This means \( y \) can be either \( 18 \) or \( -18 \).

### Step 5: Compare the values of \( x \) and \( y \)

Now we have:

- \( x = 14 \)
- \( y = 18 \) or \( y = -18 \)

We can compare \( x \) with both possible values of \( y \):

1. When \( y = 18 \):
\[ 14 < 18 \quad \text{(So, } x < y\text{)} \]

2. When \( y = -18 \):
\[ 14 > -18 \quad \text{(So, } x > y\text{)} \]

### Conclusion

Since \( x \) is less than \( y \) in one case and greater than \( y \) in another case, we cannot establish a consistent relationship between \( x \) and \( y \). Therefore, the answer is:

**No relation between \( x \) and \( y \)**.

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