Between what two consecutive numbers does the square root 85 lie?
The Correct Answer and Explanation is:
The square root of 85 lies between 9 and 10.
Explanation
To determine between which two consecutive numbers the square root of 85 lies, we start by identifying perfect squares near 85. A perfect square is a number that is the square of an integer. For example, 81 is a perfect square because it equals 9 × 9, and 100 is also a perfect square because it equals 10 × 10.
Now let’s analyze this step by step:
- The square root of 81 is exactly 9 because 9 × 9 = 81.
- The square root of 100 is exactly 10 because 10 × 10 = 100.
Since 85 is greater than 81 and less than 100, its square root must be greater than 9 but less than 10. Therefore, √85 lies between the numbers 9 and 10.
We can confirm this more precisely with some approximations:
- Try 9.1:
9.1 × 9.1 = 82.81
Still less than 85, so √85 > 9.1 - Try 9.2:
9.2 × 9.2 = 84.64
Still less than 85, so √85 > 9.2 - Try 9.3:
9.3 × 9.3 = 86.49
Now greater than 85, so √85 < 9.3
So, from this approximation, we can say the square root of 85 is somewhere between 9.2 and 9.3. But since the question asks for consecutive whole numbers, we do not need to find a decimal approximation. We only need to know between which two whole numbers √85 lies.
Therefore, the final answer is:
The square root of 85 lies between 9 and 10.
