Find the cubic root of 108
The cubic root of 108 is approximately 4.3267487109222245.
To find the cubic root of 108, you can use a calculator or follow these steps manually:
1. Start with an initial guess for the cubic root of 108. Let's choose 4 as an initial guess.
2. Divide 108 by the initial guess: 108 ÷ 4 = 27.
3. Take the average of the quotient and the initial guess: (27 + 4) ÷ 2 = 15.5.
4. Use this average as your new guess for the cubic root and repeat step 2 and 3 until you get an accurate result.
- Divide 108 by 15.5: 108 ÷ 15.5 = 6.9677419.
- Take the average of 15.5 and 6.9677419: (15.5 + 6.9677419) ÷ 2 = 11.2338709.
5. Repeat step 4 until you obtain a satisfactory level of accuracy. Continuing the process manually:
- Divide 108 by 11.2338709: 108 ÷ 11.2338709 = 9.6164647.
- Take the average of 11.2338709 and 9.6164647: (11.2338709 + 9.6164647) ÷ 2 = 10.4251678.
- Divide 108 by 10.4251678: 108 ÷ 10.4251678 = 10.374818.
- Take the average of 10.4251678 and 10.374818: (10.4251678 + 10.374818) ÷ 2 = 10.399992.
- Divide 108 by 10.399992: 108 ÷ 10.399992 = 10.384603.
- Take the average of 10.399992 and 10.384603: (10.399992 + 10.384603) ÷ 2 = 10.392297.
The approximate cubic root of 108 is 10.392297.
To find the cubic root of 108, you can use a calculator or follow these steps manually:
1. Start by making an initial guess for the cubic root. In this case, we can choose an easy value such as 2.
2. Cube the guess value. In this case, 2 cubed is equal to 8.
3. Compare the cubed guess with the given number 108. If the cubed guess is less than 108, we know that the actual cubic root is higher than our guess.
4. Increase the guess value slightly and repeat steps 2 and 3 until we find a value whose cube is equal to or slightly greater than 108.
Let's follow these steps:
- If we guess 2 as the cubic root, it is too low because 2 cubed is 8, which is less than 108.
- Let's try guessing 3 as the cubic root. If we cube 3, we get 27, which is again less than 108.
- Now, guess 4. Cubing 4 gives us 64, still less than 108.
- We can now try 5 as the guess. If we cube 5, we get 125, which is greater than 108.
- Since 5 cubed is 125, which is larger than 108, we can conclude that the cubic root of 108 is between 4 and 5.
So, the approximate cubic root of 108 is between 4 and 5.