Final Answer:
The square root of 40 between two positive consecutive integers is A) Between 6 and 7.
Step-by-step explanation:
To find out between which pair of consecutive positive integers the square root of 40 lies, we can begin by considering the squares of these integers:
- The square of 5 is (5² = 25),
- The square of 6 is (6² = 36),
- The square of 7 is (7² = 49),
- The square of 8 is (8² = 64).
Now, the square root of 40 is going to fall between the square root of two consecutive squares where one square is less than 40 and the next square is greater than 40.
From our list:
- 36 is the closest square that is less than 40. The square root of 36 is 6.
- 49 is the closest square that is greater than 40. The square root of 49 is 7.
Since 40 is between 36 and 49, the square root of 40 must be between the square roots of these two numbers, which are 6 and 7, respectively.
Therefore, the square root of 40 is between 6 and 7.
The correct answer is: A) Between 6 and 7.