To find three irrational numbers between √2 and √3, we first need to establish the approximate values of these square roots. The value of √2 is approximately 1.414 and √3 is approximately 1.732. Knowing this, we can look for numbers that fall between these two square roots.
1. **Number 1:** One straightforward example is the square root of 5, or √5, which is approximately 2.236. This, however, is outside the range of our query. Instead, we can look at expressions like:
– **Irrational number:** √(8/5) which is approximately 1.2649.
2. **Number 2:** Another example would be:
– **Irrational number:** (√2 + √3) / 2, which is approximately 1.573. This number is certainly between √2 and √3.
3. **Number 3:** Yet another option is:
– **Irrational number:** √(10/7), which is approximately 1.1955. Again, this is outside our range.
Another valid option to consider would be :
– **Irrational number:** (√3 – √2) / 2 + √2 which gives us a value around 1.5, well within our limits.
These examples, namely (√(8/5), (√2 + √3) / 2 and (√3 – √2) / 2 + √2, are anchoring irrational numbers found between √2 and √3. They showcase how we can derive numbers in this range using mathematical expressions that yield irrational results.