How to Find the Cubic Root of a Number: A Step-by-Step Guide with Newton’s Method

cubic root

The cubic root, also known as the cube root, is the mathematical operation that finds the value which, when multiplied by itself three times, gives a specific number

The cubic root, also known as the cube root, is the mathematical operation that finds the value which, when multiplied by itself three times, gives a specific number. In other words, it is the opposite of cubing a number.

To calculate the cubic root of a number, you can use a scientific calculator or math software. However, I will explain the manual process for finding the cubic root of a number.

Let’s suppose we want to find the cubic root of a number, say 125.

1. Start by making an estimate. Try to find a number whose cube is close to the given number. In this case, we know that 5 cubed is equal to 125 (5 * 5 * 5 = 125). So, 5 is a good estimate for the cubic root.

2. Now we will refine our estimate using a process called “Newton’s method.” Here’s how it works:
– Divide the given number by the previous estimate (125 ÷ 5 = 25).
– Take the average of the previous estimate and the result of the division above.
(average = (5 + 25) ÷ 2 = 15)
– Use this average as the new estimate.
(new estimate = 15)

3. Repeat step 2 until you reach an accurate enough answer. In this case, let’s go through one more iteration:
– Divide the given number by the current estimate (125 ÷ 15 ≈ 8.3333).
– Take the average of the previous estimate and the result of the division above.
(average = (15 + 8.3333) ÷ 2 ≈ 11.6666)
– Use this average as the new estimate.
(new estimate ≈ 11.6666)

4. Continue with step 3 as needed until you are satisfied with the accuracy of your answer.

In this case, after further iterations, we find that the cubic root of 125 is approximately 5.000.

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