Question

Select the correct answer from each drop-down menu. The number 72 lies between the perfect squares . So, the square root of 72 lies between the numbers, which means the square root of 72 is .

Option 1: 49 and 64, 7 and 8, a whole number
Option 2: 64 and 81, 8 and 9, a whole number
Option 3: 36 and 49, 6 and 7, an irrational number
Option 4: 81 and 100, 9 and 10, an irrational number

Answer 1

The square root of 72 lies between the integers 8 and 9, and since 72 is not a perfect square, its square root is an irrational number.

Step-by-step explanation:

When determining which two consecutive whole numbers the square root of 72 lies between, you should look at the squares closest to 72. The perfect squares closest to 72 are 64 (8²) and 81 (9²). Thus, the square root of 72 lies between 8 and 9. We can confirm this by noting that 72 is greater than 64 and less than 81. Since the square of a whole number is another whole number, and 72 is not a perfect square, the square root of 72 cannot be a whole number but rather an irrational number.

Therefore, the correct answer would be: The number 72 lies between the perfect squares 64 and 81. So, the square root of 72 lies between the numbers 8 and 9, which means the square root of 72 is an irrational number.