Find one irrational and one rational number between 2 and `sqrt(5)`

Answer

To find one rational and one irrational number between 2 and \(\sqrt{5}\), we will follow these steps:

### Step 1: Determine the value of \(\sqrt{5}\)
To find the decimal value of \(\sqrt{5}\), we can calculate it using long division or a calculator.

\[ \sqrt{5} \approx 2.236 \]

### Step 2: Identify the range
Now we have the range between 2 and \(\sqrt{5}\):
\[ 2 < x < 2.236 \]

### Step 3: Find a rational number
A rational number can be expressed as a fraction or a terminating or repeating decimal. We can choose:
\[ \text{Rational number} = 2.2 \]
This number is between 2 and \(\sqrt{5}\).

### Step 4: Find an irrational number
An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion. We can choose:
\[ \text{Irrational number} = \sqrt{5} - 0.01 \approx 2.226 \]
This number is also between 2 and \(\sqrt{5}\).

### Final Answer
Thus, one rational number is \(2.2\) and one irrational number is approximately \(2.226\).

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