What is the difference between a radical and a rational expression in math?

A rational expression is a polynomial fraction, and anything you could do with regular fractions you can do with rational expressions. However, since there are variables in rational expressions, there are some additional considerations.

When you dealt with fractions, you knew that the fraction could have any whole numbers for the numerator and denominator, as long as you didn't try to divide by zero. When dealing with rational expressions, you will often need to evaluate the expression, and it can be useful to know which values would cause division by zero, so you can avoid these x-values. So probably the first thing you'll do with rational expressions is find their domains.

Here are some examples of rational expressions:

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Rational Expressions via kwout

While a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root or higher.

When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol. For example, 3√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.

The term underneath the radical symbol is called the radicand.

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Wednesday, March 29 2017
Source: http://www.purplemath.com/modules/rtnldefs.htm