Find the square root of 96.
The square root of 96 is approximately 9.80
To find the square root of 96, follow these steps:
Step 1: Start by estimating the square root of 96. The closest perfect square to 96 is 81, with a square root of 9.
Step 2: Divide 96 by 81. The result is approximately 1.185.
Step 3: Calculate a better estimate by finding the average of 9 and 1.185. The average is approximately 5.092.
Step 4: Square the better estimate from step 3. The result is approximately 25.925.
Step 5: Check if the square of the estimate is close enough to 96. Since 25.925 is less than 96, the estimate is too low.
Step 6: Adjust the estimate higher and repeat steps 4 and 5. Repeat this process until the estimate is close enough.
Step 7: By adjusting the estimate, we find that the square root of 96 is approximately 9.798.
Therefore, the square root of 96 is approximately 9.798.
To find the square root of 96, you can use the following steps:
1. Start by guessing a number that, when squared, is close to but less than 96. Let's start with 9 since 9^2 = 81.
2. Divide 96 by 9. The result is 10.6667.
3. Take the average of the guess (9) and the result (10.6667). The average is 9.8333.
4. Repeat steps 2 and 3, using the new average as the guess, until you reach a satisfactory level of precision.
Let's go through the process a few more times:
Guess = 9
96 divided by 9 = 10.6667
New average = (9 + 10.6667) / 2 = 9.8333
Guess = 9.8333
96 divided by 9.8333 = 9.7692
New average = (9.8333 + 9.7692) / 2 = 9.8013
Guess = 9.8013
96 divided by 9.8013 = 9.7994
New average = (9.8013 + 9.7994) / 2 = 9.8003
As you can see, the average is approaching a fixed value. By continuing this process for more iterations, you can achieve a more accurate estimate. In this case, after several iterations, you'll find that the value converges to approximately 9.79796. Therefore, the square root of 96 is approximately 9.79796.