How to Find Cubic Roots
- 1). Use a calculator if available to solve for the cubic root. This is the fastest and preferred way to find a cubic root. Press the cubic root symbol on a calculator (an advanced calculator like a graphing calculator will have a cubic root symbol). Then press the number for which you want to find the cubic root and press "enter." You have your cubic root.
- 2). Use your memory if you do not have a calculator available. It is recommended that you memorize perfect roots because they are the most likely to come up in exams and are easy to remember. A perfect root is like 9, its cubic root is a whole number. The cubic roots for numbers 1 through 12 are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000, 1,331 and 1,728.
- 3). Memorize the "endings" of the cubes. This knowledge is helpful when you are stuck on multiple choice questions. If you know the pattern of cubic endings then you will be able to use the process of elimination to narrow down your answer choices. The cubic ending pattern for numbers one through nine respectively are: 1, 8, 7, 4, 5, 6, 3, 2 and 9. For example, if you are asked to find the cubic root of 729, you will immediately know that the last number of the root is 9 because the last digit of the original number is 9 (the answer actual is 9).
- 4). Estimate the cubic root as best as you can without a calculator. There is no formula to find a cubic root and the calculator just performs guess and check work very fast. First, ballpark the cubic root by finding the nearest perfect cubic root. For example, if asked to find the cubic root of 29, you find the closest perfect cubic root, which is 27 and the root is 3. Try a number slightly higher than 3.1 and multiply by it three times (3.1*3.1*3.1= 29. 791). The number is too high so try a smaller one, 3.07*3.07*3.07=29.934443. You can try it make it closer, like trying 3.72*3.72*3.72=28.9910292. That's pretty close.
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