Insert two rational numbers and two irrational numbers between ` sqrt3 and sqrt 8.`

Answer

To insert two rational numbers and two irrational numbers between \( \sqrt{3} \) and \( \sqrt{8} \), we can follow these steps:

### Step 1: Determine the approximate values of \( \sqrt{3} \) and \( \sqrt{8} \)

- Calculate \( \sqrt{3} \):
\[ \sqrt{3} \approx 1.732 \]

- Calculate \( \sqrt{8} \):
\[ \sqrt{8} = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828 \]

### Step 2: Identify the range between \( \sqrt{3} \) and \( \sqrt{8} \)

- The range is from approximately 1.732 to 2.828.

### Step 3: Find two rational numbers in this range

- We can choose:
- \( 2 \) (which is between 1.732 and 2.828)
- \( \frac{12}{5} = 2.4 \) (which is also between 1.732 and 2.828)

### Step 4: Find two irrational numbers in this range

- We can choose:
- \( \sqrt{5} \) (since \( \sqrt{5} \approx 2.236 \), which is between 1.732 and 2.828)
- \( \sqrt{7} \) (since \( \sqrt{7} \approx 2.646 \), which is also between 1.732 and 2.828)

### Final Answer

The two rational numbers are \( 2 \) and \( \frac{12}{5} \), and the two irrational numbers are \( \sqrt{5} \) and \( \sqrt{7} \).

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