find two irrational numbers lying between root of 2 and root of 3
the mean of two values lies between them. So, (√2+√3)/2 does the job.
Or, just note that
√2 = 1.414...
√3 = 1.732...
Now pick any value in between them.
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To find two irrational numbers lying between the square root of 2 (√2) and the square root of 3 (√3), we can use a property of irrational numbers: between any two irrational numbers lies an infinite number of other irrational numbers.
Here's how we can find two such numbers:
1. Start with √2 and √3:
- √2 ≈ 1.4142
- √3 ≈ 1.7321
2. Find the average of these two numbers:
- Average = (1.4142 + 1.7321) / 2 ≈ 1.5731
3. The average of two irrational numbers is always irrational. So, we have our first irrational number between √2 and √3, which is approximately 1.5731.
4. Now, find the average of √2 and this new number we found:
- Average = (1.4142 + 1.5731) / 2 ≈ 1.4937
5. Again, this average is irrational, and it lies between √2 and √3. So, we have our second irrational number between √2 and √3, which is approximately 1.4937.
Therefore, two irrational numbers lying between √2 and √3 are approximately 1.5731 and 1.4937. Note that there are infinitely many other irrational numbers between these two values.
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