How to Simplify Radicals Into Decimals

By Tricia Lobo

Radicals, which are the roots of numbers, are an important concept in algebra that will continue to come up throughout upper-level math and engineering classes. If you have a memory for perfect squares and cubes, then certain kinds of radicals will have very familiar answers. For instance, SQRT(4) is 2 and SQRT(81) is 9. When working with radicals that you want to simplify to decimals, you either need to remember the decimal equivalent with the radical -- which will happen when you work with radicals frequently over a long period of time -- or you need a calculator.



Separate the radical into its constituent perfect squares and cubes, if relevant. If working with the square root of 50, for instance, you may rewrite SQRT(50) as SQRT(25)_SQRT(2), equal to 5_SQRT(2).

Recall the value of SQRT(2), or look it up in a table of radicals. SQRT(2) is approximately equal to 1.41, so you may multiply 5 by 1.41, by hand or by calculator, to obtain 7.05.

Plug SQRT(50) into a scientific or graphing calculator, to check the conversion that you carried out in Step 2.

About the Author

Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.