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.