square root of 68 rounded to the nearest hundredth
8.25
To find the square root of 68, rounded to the nearest hundredth, follow these steps:
1. Start with an initial guess. Let's choose the number 8.
2. Divide 68 by the initial guess: 68 divided by 8 equals 8.5.
3. Calculate the average of the initial guess and the result obtained in step 2: (8 + 8.5) / 2 equals 8.25.
4. Repeat steps 2 and 3 using the new result (8.25) as the guess.
Continue this process until you achieve the desired level of accuracy. In this case, let's go to two decimal places:
5. Divide 68 by the current guess: 68 divided by 8.25 equals 8.24242424... (continue this pattern).
6. Calculate the average of the current guess (8.25) and the result obtained in step 5: (8.25 + 8.24242424) / 2 equals 8.24621212... (continue this pattern).
Once you have the desired level of accuracy, round the result to the nearest hundredth:
The square root of 68, rounded to the nearest hundredth, is approximately 8.25.