if `y^(2)` = 625 then y is

Options

A. a rational number
B. an irrational number
C. neither rational nor irrational
D. a natural number

Answer

To solve the equation \( y^2 = 625 \), we will follow these steps:

### Step 1: Write down the equation
We start with the equation given in the problem:
\[ y^2 = 625 \]

### Step 2: Take the square root of both sides
To find the value of \( y \), we take the square root of both sides of the equation:
\[ y = \sqrt{625} \]

### Step 3: Calculate the square root
Next, we calculate the square root of 625. We know that:
\[ \sqrt{625} = 25 \]
Thus, we have:
\[ y = 25 \]

### Step 4: Consider both positive and negative roots
Since we are dealing with a square, we must consider both the positive and negative roots:
\[ y = \pm 25 \]

### Step 5: Identify the type of numbers
Now, we need to determine what kind of numbers \( y \) can be:
- The values of \( y \) are \( 25 \) and \( -25 \).
- Both \( 25 \) and \( -25 \) are rational numbers because they can be expressed as fractions (e.g., \( 25 = \frac{25}{1} \) and \( -25 = \frac{-25}{1} \)).
- However, \( -25 \) is not a natural number since natural numbers are positive integers.

### Conclusion
Thus, the final answer is:
\[ y = 25 \text{ or } y = -25 \]
And both values of \( y \) are rational numbers.