Question

Finding the cube root of a number 512 by successive subtraction method

Answer 1

To find the cube root of a number using successive subtraction, you start with an initial guess and keep subtracting smaller numbers until you approach the cube root. With an initial guess of 10, subtract 512 from the cube of the guess, update the guess, and repeat until you get close to the cube root.

Step-by-step explanation:

To find the cube root of a number 512 using the successive subtraction method, we can start with an initial guess and repeatedly subtract smaller numbers until we get close to the cube root. Let's start with an initial guess of 10.

1. Cube 10: 10 * 10 * 10 = 1000
2. Subtract: 1000 - 512 = 488
3. Update guess: 10 - 1 = 9
4. Cube 9: 9 * 9 * 9 = 729
5. Subtract: 729 - 512 = 217
6. Update guess: 9 - 0.1 = 8.9
7. Cube 8.9: 8.9 * 8.9 * 8.9 = 682.929
8. Subtract: 682.929 - 512 = 170.929

Continuing this process, we can eventually get closer and closer to the cube root, which is approximately 8. :)

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