"

Unit 6.1 Introduction to Radicals and Simplifying Radical Expressions

Radicals

In mathematics, a radical expression is an expression that includes a radical symbol (√), which indicates a root. The most common radical is the square root, but radicals can also denote cube roots, fourth roots, and higher-order roots. This is often called the “nth” root
Components of a Radical Expression
  • Radical Symbol (√): Indicates the root being taken.
  • Radicand: The number or expression inside the radical symbol.
  • Index: Indicates the degree of the root.
    • If no index is shown, it is assumed to be 2 (square root)

Radical Rules

Simplifying Radical Expressions with Perfect nth Roots

[latex]\sqrt[n]{a^n} = a[/latex]

 

Product Rule of Radical Expressions

[latex]\sqrt[n]{a \cdot b} = \sqrt[n]{a} \cdot \sqrt[n]{b}[/latex]

 

Quotient Rule of Radical Expressions

[latex]\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}, \quad b \neq 0[/latex]

 

Simplifying Radical Expression with a Perfect nth root

[latex]\sqrt{16} = 4[/latex]

[latex]\sqrt[3]{27} = 3[/latex]

[latex]\sqrt[4]{16} = 2[/latex]

Simplifying Radical Expression with a non – perfect nth root

Break apart the larger number into smaller components, find a value that is a perfect root

For example 72 can be broken down into 36 times 2. 36 is a perfect square so we are able to simplify it

[latex]\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}[/latex]

 

 

License

ESET1140: Intermediate Technical Algebra Copyright © 2024 by froenico. All Rights Reserved.