Find two irrational numbers between 0.2 and 0.23.

Explanation

To find two irrational numbers between 0.2 and 0.23, we can follow these steps:

### Step 1: Identify the range
We need to find two irrational numbers that lie between 0.2 and 0.23.

### Step 2: Choose a number slightly greater than 0.2
Let's take a number slightly greater than 0.2. A good choice is 0.21.

### Step 3: Create an irrational number
To create an irrational number, we can use the square root of a non-perfect square. For example, we can take the square root of 2 and divide it by 10, then add it to 0.2:

\[ x = 0.2 + \frac{\sqrt{2}}{100} \approx 0.2 + 0.01414 \approx 0.21414 \]

### Step 4: Choose a number slightly less than 0.23
Now, let's take a number slightly less than 0.23. A good choice is 0.22.

### Step 5: Create another irrational number
Similarly, we can create another irrational number by taking the square root of 3 and dividing it by 100, then adding it to 0.2:

\[ y = 0.2 + \frac{\sqrt{3}}{100} \approx 0.2 + 0.01732 \approx 0.21732 \]

### Step 6: Verify the numbers
Now we have two numbers:
1. \( x \approx 0.21414 \)
2. \( y \approx 0.21732 \)

Both of these numbers are between 0.2 and 0.23, and they are irrational because they cannot be expressed as a fraction of two integers.

### Final Answer
The two irrational numbers between 0.2 and 0.23 are approximately:
1. \( 0.21414 \)
2. \( 0.21732 \)