What is the least integer whose square root is an irrational number between 5 and 7?
13
6
26
25
The square root of 25 is 5, which is not between 5 and 7.
The square root of 26 is an irrational number, but it is not between 5 and 7.
The square root of 6 is an irrational number, but it is not between 5 and 7.
The square root of 13 is an irrational number and is between 5 and 7.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 13.
So the correct answer is 13.
To find the least integer whose square root is an irrational number between 5 and 7, we need to determine the integers whose square roots fall within this range.
First, we find the square root of 5: √5 ≈ 2.236.
Then, we find the square root of 7: √7 ≈ 2.646.
Now we need to find the least integer whose square root is greater than 2.236 and less than 2.646.
The next integer after 2.236 is 3. However, √9 = 3, which is not within the desired range.
The next integer after 3 is 4. However, √16 = 4, which is also not within the desired range.
The next integer after 4 is 5. √25 = 5, which is within the desired range.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 25.