Find the square root of 85 correct to the nearest tenth

Find the square root of 85 correct to the nearest tenth.
A. 9.10
B.9.20
C. 9.30
D. 9.40

The Correct Answer and Explanation is :

To find the square root of 85 correct to the nearest tenth, we can follow these steps:

1. Understanding Square Roots: The square root of a number ( x ) is a value ( y ) such that ( y^2 = x ). In this case, we are looking for ( y = \sqrt{85} ).
2. Estimating the Square Root: We know that ( 9^2 = 81 ) and ( 10^2 = 100 ). Therefore, the square root of 85 lies between 9 and 10.
3. Refining the Estimate: To narrow it down, we can test numbers between 9 and 10. Let’s start by testing 9.2: [
   9.2^2 = 9.2 \times 9.2 = 84.64
   ] Since 84.64 is less than 85, we know that ( \sqrt{85} ) is greater than 9.2.
4. Testing 9.3: [
   9.3^2 = 9.3 \times 9.3 = 86.49
   ] Here, 86.49 is greater than 85, indicating that ( \sqrt{85} ) is less than 9.3.
5. Further Testing Between 9.2 and 9.3: We can now test a value closer to 9.2, such as 9.25. [
   9.25^2 = 9.25 \times 9.25 = 85.5625
   ] This result shows that 85.5625 is greater than 85. Next, we try 9.23: [
   9.23^2 = 9.23 \times 9.23 = 85.1529
   ] This is still greater than 85. Lastly, let’s try 9.21: [
   9.21^2 = 9.21 \times 9.21 = 84.9441
   ] This value is less than 85. From our tests, we have determined:

• ( 9.21^2 < 85 )
• ( 9.23^2 > 85 )

1. Conclusion: Since 9.22 would yield a square closer to 85, we can conclude that the square root of 85 is approximately ( 9.22 ), which, when rounded to the nearest tenth, gives us 9.3.

Thus, the answer is C. 9.30.