Find the cube root of 81.

The cube root of 81 is 4.

To find the cube root of a number, we need to find the number that, when multiplied by itself twice, gives the original number.

To find the cube root of 81, we can start by trying to factorize 81. We can see that 81 can be expressed as 3 * 3 * 3 * 3.

So, the cube root of 81 is 3.

In general, to find the cube root of a number, you can factorize the number into prime factors and look for groups of three identical prime factors. The product of those prime factors will be the cube root of the original number.

To find the cube root of 81, follow these steps:

Step 1: Start with an initial guess for the cube root. Let's start with the guess of 2.

Step 2: Divide 81 by the initial guess:

81 ÷ 2 = 40.5

Step 3: Calculate a better estimate for the cube root by taking the average of the initial guess and the result from Step 2:

(2 + 40.5) ÷ 2 = 21.25

Step 4: Repeat steps 2 and 3, using the new estimate in place of the initial guess, until you get a precise enough answer.

(81 ÷ 21.25) = 3.82
(21.25 + 3.82) ÷ 2 = 12.03
(81 ÷ 12.03) = 6.72
(12.03 + 6.72) ÷ 2 = 9.38
(81 ÷ 9.38) = 8.64
(9.38 + 8.64) ÷ 2 = 9.01
(81 ÷ 9.01) = 8.99

Step 5: The cube root of 81 is approximately 9.