Find the cube root of 43.

The cube root of 43 can be approximated to three decimal places as follows:

1. Start with an initial guess. A good initial guess can be the nearest integer to the cube root of 43, which is 3.
2. Divide 43 by the initial guess raised to the power of 2 (i.e., 3^2 = 9). This gives (43 / 9) = 4.777.
3. Average the initial guess and the result of step 2. This gives (3 + 4.777) / 2 = 3.8885.
4. Repeat steps 2 and 3 using the result of step 3 as the new guess until the desired level of accuracy is achieved.

Using this process, we get:

• Guess 1: 3
• Guess 2: (3 + 4.777) / 2 = 3.8885
• Guess 3: (3.8885 + (43 / 3.8885^2)) / 2 = 3.4971
• Guess 4: (3.4971 + (43 / 3.4971^2)) / 2 = 3.5262
• Guess 5: (3.5262 + (43 / 3.5262^2)) / 2 = 3.5268

So the cube root of 43 to three decimal places is approximately 3.527.