To find three irrational numbers between the square roots of 2 and 3, we first need to establish the numerical values of these square roots. √2 is approximately 1.414 and √3 is approximately 1.732.
Now, we can look for irrational numbers in this interval. One simple method is to take averages or combinations of these numbers. Here are three examples:
- 1.5 (which is rational, but we can take an average to locate irrational numbers like 1.4 + 0.1 and square root the sum)
- √(2.1) = 1.449 (an irrational number)
- √(2.5) = 1.581 (another irrational number)
- √(2.8) = 1.673 (yet another irrational number)
All of these numbers are between √2 and √3 and are irrational. By taking square roots of numbers that are not perfect squares between 2 and 3, we can easily find irrational numbers.