Find a rational number between `sqrt2 and sqrt3.`

Answer

To find a rational number between \(\sqrt{2}\) and \(\sqrt{3}\), we can follow these steps:

### Step 1: Determine the approximate values of \(\sqrt{2}\) and \(\sqrt{3}\).
- The approximate value of \(\sqrt{2}\) is about \(1.414\).
- The approximate value of \(\sqrt{3}\) is about \(1.732\).

### Step 2: Identify a range between \(\sqrt{2}\) and \(\sqrt{3}\).
- The range we are considering is from \(1.414\) to \(1.732\).

### Step 3: Choose a rational number within this range.
- We can select a number that is clearly between \(1.414\) and \(1.732\). For example, \(1.5\) is a good choice.

### Step 4: Express the chosen rational number in the form \(\frac{p}{q}\).
- The number \(1.5\) can be expressed as \(\frac{3}{2}\).

### Conclusion:
Thus, a rational number between \(\sqrt{2}\) and \(\sqrt{3}\) is \(\frac{3}{2}\) or \(1.5\).

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