Radicals

A radical is an expression of the type Radical, where n is the index and a is the radicand.

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

Radical-Exponent

Radicals

Simplifying Radicals

Simplifying Radicals

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


The inverse operation can also be performed.

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Introduction of Factors

Addition and Subtraction of Radicals

Two radicals can only be added (or subtracted) when they have the same index and radicand, that is to say, they are similar radicals.

Equivalent Radicals

Example

Radical Exercise

Radical Solution


Multiplication of Radicals

Same Index

To multiply radicals with the same index, multiply the radicands and the index remains the same.

Multipliying Radicals

Multipliying Radicals

Multipliying Radicals

Different Index

First, reduce to a common index and then multiply.

1.The 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

Examples

Different Index Multiplication

Different Index Multiplication

Different Index Multiplication

Different Index Multiplication

Different Index Multiplication

Multipliying Radicals


Division of Radicals

Same Index

To divide radicals with the same index, divide the radicands and the same index is used for the resultant radicand.

Division with the Same Index

Dividing Radicals

Dividing Radicals

Different Index

Reduce to a common index and divide.

Examples

Dividing Radicals

Dividing Radicals

Dividing Radicals

Dividing Radicals

Dividing Radicals