Radicals

A radical is an expression denoted as Radical, in which nPerteneceNatural Number and aPerteneceReal Number; so that when a is negative, n must be odd.

Radical

Radicals

Powers and Radicals

A radical can be expressed in the form of a power:

Radical-Exponent

Radicals

Equivalent Radicals

Using the notation of a fractional exponent and the property which says that if you multiply the numerator and denominator by the same number, the fraction is equivalent and the following is obtained:

Equivalent Radicals

If you multiply or divide the index and the exponent of a radical by the same natural number, obtained is another equivalent radical.

Equivalent Radicals

Simplifying Radicals

If there is a natural number that divides the index and the exponent (or the exponents) of a radicand, you get a simplified radical.

Simplifying Radicals

Common Index

1The common index is the least common multiple of the indices.

2 Divide the common index by each of the indices and each result is multiplied by their corresponding exponents.

Common Index

Common Index

Common Index

Common Index

Extraction of Factors

1 If an exponent is lower than the index, the factor is left in the radicand

Extraction of Factors

Extraction of Factors

2 If an exponent is equal to the index, the factor goes outside the radicand.

Extraction of Factors

Extraction of Factors

3 If an exponent is greater than the index and is divided by the index, the quotient is the exponent of the factor outside the radicand and the remainder is the exponent of the factor within the radicand.

Extraction of Factors

Extraction of Factors

Extraction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors