Which is the rational number from the following ?

Options

A. `sqrt(7)`
B. `sqrt(8)`
C. `sqrt(9)`
D. `sqrt(10)`

Answer

To determine which of the given options is a rational number, we need to understand the definition of rational and irrational numbers. A rational number is any number that can be expressed as the quotient or fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). An irrational number, on the other hand, cannot be expressed in this form.

Let's analyze the options step by step:

### Step 1: Identify the options
Assuming the options are:
1. \( \sqrt{2} \)
2. \( \sqrt{8} \)
3. \( \sqrt{9} \)
4. \( \sqrt{10} \)

### Step 2: Evaluate each option

**Option 1: \( \sqrt{2} \)**
- The square root of 2 is not a perfect square. It cannot be expressed as a fraction of two integers. Therefore, \( \sqrt{2} \) is an **irrational number**.

**Option 2: \( \sqrt{8} \)**
- We can simplify \( \sqrt{8} \):
\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \]
- Since \( \sqrt{2} \) is irrational, \( 2\sqrt{2} \) is also irrational. Thus, \( \sqrt{8} \) is an **irrational number**.

**Option 3: \( \sqrt{9} \)**
- The square root of 9 is a perfect square:
\[ \sqrt{9} = 3 \]
- Since 3 is an integer, it can be expressed as \( \frac{3}{1} \). Therefore, \( \sqrt{9} \) is a **rational number**.

**Option 4: \( \sqrt{10} \)**
- The square root of 10 is not a perfect square. It cannot be expressed as a fraction of two integers. Therefore, \( \sqrt{10} \) is an **irrational number**.

### Conclusion:
From the analysis, the only rational number among the options is:
- **Option 3: \( \sqrt{9} \)**