What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
13
13
26
26
25
25
6
25
To find the least integer whose square root is an irrational number between 5 and 7, we need to calculate the square of each integer until we find one whose square root meets the given condition.
Starting with the smallest integer in the given range, we have:
- For 5, the square is 25, which is not between 5 and 7.
- For 6, the square is 36, which is not between 5 and 7.
- For 7, the square is 49, which is not between 5 and 7.
Continuing with the next integer:
- For 8, the square is 64, which is not between 5 and 7.
- For 9, the square is 81, which is not between 5 and 7.
- For 10, the square is 100, which is not between 5 and 7.
We can see that the square of each integer up to 10 is not within the given range. Therefore, we need to continue checking higher integers.
- For 11, the square is 121, which is not between 5 and 7.
- For 12, the square is 144, which is not between 5 and 7.
- For 13, the square is 169, which is between 5 and 7.
So, the least integer whose square root is an irrational number between 5 and 7 is 13.
Hence, the correct answer is 13.