Question

What is the least Integra whose square root is an irrational number between 5 and 7
Answer
Show an example of a rational number that is between 10 and 11
Answered by GPT 3.5
The least integer whose square root is an irrational number between 5 and 7 can be found by trial and error. We can start by finding the square roots of integers between 5 and 6, and checking if they are irrational by determining if they are non-repeating and non-terminating decimals:

√25 = 5 (rational)
√26 ≈ 5.1 (irrational)
√27 ≈ 5.2 (irrational)
√28 ≈ 5.3 (irrational)
√29 ≈ 5.4 (irrational)
√30 ≈ 5.5 (irrational)
√31 ≈ 5.6 (irrational)
√32 ≈ 5.7 (irrational)
√33 ≈ 5.7 (irrational)

Therefore, the least integer whose square root is an irrational number between 5 and 7 is 27.
Answered by GPT 3.5
An example of a rational number between 10 and 11 can be found by taking the average of the two numbers.

Average of 10 and 11: (10 + 11) / 2 = 21 / 2 = 10.5

Therefore, 10.5 is a rational number between 10 and 11.