Question

Without a calculator, determine which is greatest, √94 or 10. Explain your reasoning.

A. √94 is greater because 94 is closer to 100 than 10.
B. 10 is greater because 94 is less than 100.
C. √94 is greater because the square root makes the number smaller.
D. 10 is greater because it is a whole number.

Answer 1

The square root of 94 is between 9 and 10, as 94 is between 81 (9²) and 100 (10²). Since 94 is less than 100, its square root is less than 10, thus 10 is greater than √94.

Step-by-step explanation:

To determine which is greater, √94 or 10 without using a calculator, we should consider the closest perfect squares to 94, which are 81 (9²) and 100 (10²). Since 94 is between 81 and 100, its square root must be between 9 and 10. Given that 10 is the square root of 100, and since 94 is less than 100, √94 must be less than 10. Therefore, 10 is greater than √94. The correct answer is B: 10 is greater because 94 is less than 100.