Radical Notations: If is a real number, is a positive integer, and is a real number, then

In the radical , the symbol is a radical sign, the number is the radicand and is the index. Usually we denote as If is a real number, is an integer, is a positive integer, and is a real number, then

Rules for Radicals: For all real numbers and , and positive integers and for which the indicated roots are real numbers:

1. Product Rule:
2. Quotient Rule: ,
3. Power Rule:

Rationalizing Denominators: No denominator contain a radical.

Exs. ,

Simplified Radicals: An expression with radicals is simplified when all of the following conditions are satisfied.

1. The radicand has no factor raised to a power greater than or equal to the index.

Ex. .

2. The radicand has no fractions.

Exs. , .

3. The denominator is rationalized.

Exs. , .

4. Exponents in the Radicand and the index of the radical have no common factor.

Ex. .

5. All indicated operations have been performed (if possible).

Ex. .

Like Radicals: Radicals with the same radicand and the same index.

Ex. and are like radicals.

Subsections

Department of Mathematics