## Cubed Root Calculator

## Definition – What is a cubed root?

The cubed root of a number is the number that, when multiplied by itself three times (number x number x number), gives the original number.

For example, the cubed root of 27 is 3, as 3 x 3 x 3 = 27.

The cubed root of 125 is 5, as 5 x 5 x 5 = 125.

Unlike the square root, the cubed root is always positive.

The opposite of the cubed root is a cubed (power of 3) calculation.

In geometry cubed root can be used to find the length of a side of a cubed when the volume is known.

## Formula – How to calculate the cubed root of a number

There is no quick formula to calculate a cubed root. Most calculators use some form of trial and error.

### Trial and Error

Most calculators use trial and error to find a cubed root. Trial and error works well for perfect cubes. It can be very time consuming for non-perfect cubes because there are many decimal places.

To find cubed root by trial and error:

- Guess a number that you think could be the cubed root
- Multiply the number x number x number.
- If the result is too low, guess another higher number. If the result is too high, guess another lower number.
- Keep repeating until you find the cubed root.

Example – Find the cubed root of 512 using trial and error:

- Try a number – 5 : 5 x 5 x 5 = 125 (too low)
- Try a number that is more than 5 – 10 – 10 x 10 x 10 = 1,000 (too high)
- Try a number between 5 and 10 – 8 – 8 x 8 x 8 = 512 (answer)

### Method 2 – Quickly find roots from perfect cube numbers

This method makes it quicker to find the root of a perfect cube number. If the number is not a perfect cube root number, however, this method won’t give an answer.

## How do you type cubed root?

- On a windows keyboard, enter a 3. Select the number, and the “font” option in your program, and set the font of the 3 to “superscript.” Next, open the character map, find the square root symbol, and copy/paste it to the document.
- On a mac keyboard, enter a 3. Select the number, and the “font” option in your program, and set the font of the 3 to “superscript.” Next, press option+v for the square root symbol.
- In an HTML or web document, surround the “3” with <sup> tags (<sup>3</sup>). After the 3 use the square root symbol √.

## Cubed Root Number Table – Perfect Cubes

^{3}√1 = 1, as 1 x 1 x 1 = 1^{3}√8 = 2, as 2 x 2 x 2 = 8^{3}√27 = 3, as 3 x 3 x 3 = 27^{3}√64 = 4, as 4 x 4 x 4 = 64^{3}√125 = 5, as 5 x 5 x 5 = 125^{3}√216 = 6, as 6 x 6 x 6 = 216^{3}√343 = 7, as 7 x 7 x 7 = 343^{3}√512 = 8, as 8 x 8 x 8 = 4096^{3}√729 = 9, as 9 x 9 x 9 = 729^{3}√1000 = 10, as 10 x 10 x 10 = 1,000^{3}√1331 = 11, as 11 x 11 x 11 = 1,331^{3}√1728 = 12, as 12 x 12 x 12 = 1,728^{3}√3375 = 15, as 15 x 15 x 15 = 3,375^{3}√4913 = 17, as 17 x 17 x 17 = 4,913^{3}√8000 = 20, as 20 x 20 x 20 = 8,000^{3}√15625 = 25, as 25 x 25 x 25 = 15,625^{3}√27000 = 30, as 30 x 30 x 30 = 27,000^{3}√35936 = 33, as 33 x 33 x 33 = 35,936^{3}√91125 = 45, as 45 x 45 x 45 = 91,125^{3}√125000 = 50, as 50 x 50 x 50 = 125,000^{3}√216000 = 60, as 60 x 60 x 60 = 216,000^{3}√421875 = 75, as 75 x 75 x 75 = 421,875^{3}√1000000 = 100, as 100 x 100 x 100 = 1,000,000

## Cubed Root Number Table

## Sources and more resources

- Wikipedia – Cube root, nth root, and Cube (algebra) detail the calculations involved with cube roots.
- An introduction to cube roots from MathIsFun, Cliffs Notes, and Wolfram MathWorld.
- A video introduction to cube roots from Khan Academy.
- How to calculate cube roots from Khan Academy and MindYourDecisions.