How To Simplify Radicals Into Decimals

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.

Step 1

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).

Step 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.

Step 3

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