Cube Root

Pronunciation: /kjub rut/ Explain

The cube root of an arbitrary value x is a value that, when multiplied by itself three times, equals x.^[1] Stated mathematically, .

While a square root of a negative number is undefined for real numbers, the cube root of a negative number is possible. This is because a negative number multiplied by itself three times is still negative.

Examples of Cube Roots

Table 1

Using a Calculator to Calculate a Cube Root

While some scientific calculators have a cube root button, most do not. To calculate the cube root of 3, type the following characters into your calculator, followed by the enter key: 3^(1/3). This works because the cube root of x is the same thing as x raised to the 1/3 power: .

References

1. McAdams, David E.. All Math Words Dictionary, cube root. 2nd Classroom edition 20150108-4799968. pg 51. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. cube root. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/cube root. Buy the book
3. Oberg, Erik. Elementary Algebra. pg 8. www.archive.org. Machinery's Reference Series. The Industrial Press. 1914. Last Accessed 6/25/2018. http://www.archive.org/stream/elementaryalgebr00oberrich#page/8/mode/1up/search/cube. Buy the book
4. Hines, G. D.. Mathematical roots uprooted, including square root, cube root, and other roots. pp 3-5. www.archive.org. J. R. Holcomb & Co., Publishers. 1886. Last Accessed 6/25/2018. http://www.archive.org/stream/mathematicalroot00hinerich#page/n10/mode/1up/search/cube. Buy the book

Cite this article as:

McAdams, David E. Cube Root. 4/16/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/cuberoot.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/16/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/22/2010: Added "References". (McAdams, David E.)
11/25/2008: Changed equations to images. (McAdams, David E.)
7/11/2008: Changed equations to Hot_EQN. (McAdams, David E.)
1/5/2008: Initial version. (McAdams, David E.)