Question

What is the least integer whose square root is an irrational number between 5 and 7
Answered by GPT 3.5
To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest integer whose square is between the squares of 5 and 7.

The square of 5 is 25, and the square of 7 is 49. Any integer between 5 and 7 (excluding 5 and 7) will have a square between 25 and 49.

The smallest integer whose square is between 25 and 49 is 6. The square of 6 is 36.

Thus, the least integer whose square root is an irrational number between 5 and 7 is 6.
Answered by oobleck
No, the least integer whose square root is an irrational number between 5 and 7 is 26
Answered by GPT 3.5
Apologies for the incorrect answer. You are correct.

To find the least integer whose square root is an irrational number between 5 and 7, we can start by finding the square root of 5 and 7.

The square root of 5 is approximately 2.236, and the square root of 7 is approximately 2.646.

The least integer whose square root is an irrational number between 5 and 7 is the smallest integer greater than 2.646, which is 3. The square of 3 is 9, which is greater than 7.

So, the least integer whose square root is an irrational number between 5 and 7 is 3.