Approximate square root of, 84, end square root
84
84
by following the steps below.
square root of, 84, end square root
84
84
must lie between the whole numbers
and
9 and 10.
To find a more precise approximation, we can use the following steps:
1. Take the average of the two whole numbers: (9 + 10) / 2 = 9.5
2. Square the result: 9.5 * 9.5 = 90.25
3. Compare the squared result to the original number: 90.25 is greater than 84.
4. Since the squared result is greater than the original number, the square root must be less than the average (9.5).
5. Repeat steps 1-4 with the updated range of whole numbers: 9 and 9.5.
6. Average: (9 + 9.5) / 2 = 9.25
7. Square: 9.25 * 9.25 = 85.5625
8. Comparison: 85.5625 is greater than 84.
9. The square root must be less than 9.25.
10. Repeat steps 1-4 with the updated range: 9 and 9.25.
11. Average: (9 + 9.25) / 2 = 9.125
12. Square: 9.125 * 9.125 = 83.140625
13. Comparison: 83.140625 is less than 84.
14. The square root must be greater than 9.125.
15. Repeat steps 1-4 with the updated range: 9.125 and 9.25.
16. Average: (9.125 + 9.25) / 2 = 9.1875
17. Square: 9.1875 * 9.1875 = 83.9765625
18. Comparison: 83.9765625 is less than 84.
19. The square root must be greater than 9.1875.
Using these steps, we can conclude that the square root of 84 lies between 9.1875 and 9.25.
Approximate square root of, 84, end square root
84
84
by following the steps below.
square root of, 84, end square root
84
84
must lie between the whole numbers
9
9 and
10
10 because 9, squared, equals, start box, 81, end box
9
2
=
81
9
2
=
81
and 10, squared, equals, start box, 100, end box
1
0
2
=
100
10
2
=
100
, and 84 lies between these values.
Drag square root of, 84, end square root
84
84
based on your estimate above:
Real
√84
__
_
To one decimal place, square root of, 84, end square root
84
84
must lie between
and
9.1 and 9.2.
To find a more precise approximation, we can use the following steps:
1. Take the average of 9 and 10: (9 + 10) / 2 = 9.5
2. Square the result: 9.5 * 9.5 = 90.25
3. Compare the squared result to 84: 90.25 is greater than 84.
4. Since the squared result is greater than 84, the square root must be less than 9.5.
5. Repeat steps 1-4 with the updated range of 9 and 9.5.
6. Average: (9 + 9.5) / 2 = 9.25
7. Square: 9.25 * 9.25 = 85.5625
8. Comparison: 85.5625 is greater than 84.
9. The square root must be less than 9.25.
10. Repeat steps 1-4 with the updated range of 9 and 9.25.
11. Average: (9 + 9.25) / 2 = 9.125
12. Square: 9.125 * 9.125 = 83.140625
13. Comparison: 83.140625 is less than 84.
14. The square root must be slightly greater than 9.125.
Based on these steps, we can estimate that the square root of 84 is between 9.1 and 9.2.
To two decimal places, square root of, 84, end square root
84
84
must lie between
and
9.16 and 9.17.
To find a more precise approximation, we can use the following steps:
1. Take the average of 9 and 9.2: (9 + 9.2) / 2 = 9.1
2. Square the result: 9.1 * 9.1 = 82.81
3. Compare the squared result to 84: 82.81 is less than 84.
4. Since the squared result is less than 84, the square root must be slightly greater than 9.1.
5. Repeat steps 1-4 with the updated range of 9.1 and 9.2.
6. Average: (9.1 + 9.2) / 2 = 9.15
7. Square: 9.15 * 9.15 = 83.7225
8. Comparison: 83.7225 is less than 84.
9. The square root must be slightly greater than 9.15.
10. Repeat steps 1-4 with the updated range of 9.15 and 9.2.
11. Average: (9.15 + 9.2) / 2 = 9.175
12. Square: 9.175 * 9.175 = 84.006625
13. Comparison: 84.006625 is greater than 84.
14. The square root must be slightly less than 9.175.
Based on these steps, we can estimate that the square root of 84 is between 9.16 and 9.17 when rounded to two decimal places.
To find the approximate square root of 84, follow these steps:
1. Start by identifying the two whole numbers between which the square root of 84 lies. We know that the square root of 84 is between the whole numbers:
√(81) = 9
√(100) = 10
Therefore, the square root of 84 should lie between 9 and 10.
2. To narrow down the range further, find the average of these two numbers:
(9 + 10) / 2 = 9.5
3. Now, square the average obtained in the previous step:
9.5 * 9.5 = 90.25
4. Since the square of 9.5 is greater than 84, the square root of 84 should be smaller than 9.5.
Therefore, the approximate square root of 84 lies between 9 and 9.5.
To approximate the square root of 84, you can use the following steps:
Step 1: Identify the two whole numbers between which the square root of 84 lies.
Start by finding the largest perfect square that is smaller than 84. In this case, it is 81 (which is 9 squared). The next perfect square greater than 84 is 100 (which is 10 squared). Therefore, the square root of 84 lies between 9 and 10.
Step 2: Divide the range between the two whole numbers into smaller intervals.
Divide the range between 9 and 10 into smaller intervals, such as 9.1, 9.2, 9.3, and so on.
Step 3: Evaluate the square of each interval value and compare it to 84.
Calculate the square of each interval value and compare it to 84. For example, evaluate (9.1 * 9.1), (9.2 * 9.2), and so on. Look for the value whose square is closest to 84.
Step 4: Repeat steps 2 and 3 to improve the approximation.
Continue dividing the range into smaller intervals and evaluating their squares until you reach the desired level of accuracy in your approximation.
By following these steps, you can approximate the square root of 84.