Introduction:
Irrational numbers are the numbers which cannot be expressed in the form of p/q, where p and q are integers and q is not equal to zero. In this question, we have to find three irrational numbers lying between 0.2101 and 0.2222.

Solution:
To find the irrational numbers between 0.2101 and 0.2222, we can use the following methods:

Method 1:
We know that the decimal expansion of an irrational number is non-repeating and non-terminating. So, we can use this property to find the irrational numbers between 0.2101 and 0.2222.

Step 1: Subtract 0.2101 from 0.2222
0.2222 - 0.2101 = 0.0121

Step 2: Divide 0.0121 by 4
0.0121/4 = 0.003025

Step 3: Add 0.003025 to 0.2101
0.2101 + 0.003025 = 0.213125

Step 4: Repeat steps 2 and 3 to get two more irrational numbers
0.213125 + 0.003025 = 0.21615
0.21615 + 0.003025 = 0.219175

Therefore, three irrational numbers lying between 0.2101 and 0.2222 are 0.213125, 0.21615, and 0.219175.

Method 2:
Another method to find the irrational numbers between 0.2101 and 0.2222 is by using the square root of numbers.

Step 1: Square 0.46
0.46^2 = 0.2116

Step 2: Square 0.47
0.47^2 = 0.2209

Step 3: Square 0.48
0.48^2 = 0.2304

Step 4: Take the square root of 0.2116 and 0.2209
√0.2116 = 0.4604
√0.2209 = 0.4702

Therefore, two irrational numbers lying between 0.2101 and 0.2222 are 0.4604 and 0.4702.

Conclusion:
In conclusion, we can find three irrational numbers lying between 0.2101 and 0.2222 by using the non-repeating and non-terminating property of irrational numbers or by using the square root of numbers.

0.211010010001...
0.215050050005...
0.221010010001...