Introduction: Simplify Roots and Rational Exponents
Did you know that you can take the [latex]6th[/latex] root of a number? You have probably heard of a square root, written [latex]\sqrt{}[/latex], but you can also take a third, fourth and even a [latex]5,000th[/latex] root (if you really had to). In this lesson we will learn how a square root is defined and then we will build on that to form an understanding of nth roots. We will use factoring and rules for exponents to simplify mathematical expressions that contain roots.The learning outcomes for this lesson include:
- Define and evaluate principal square roots
- Define and evaluate nth roots
- Estimate roots that are not perfect
- Define and identify a radical expression
- Convert radicals to expressions with rational exponents
- Convert expressions with rational exponents to their radical equivalent
- Simplify radical expressions using factoring
- Simplify radical expressions using rational exponents and the laws of exponents
- Define [latex]\sqrt{x^2}=|x|[/latex], and apply it when simplifying radical expressions
The learning activities for this lesson include:
- Read: Define and Evaluate Roots
- Self-Check: Define and Evaluate Roots
- Read: Radical Expressions and Rational Exponents
- Self-Check: Radical Expressions and Rational Exponents
- Read: Simplify Radical Expressions
- Self-Check: Simplify Radical Expressions
Licenses & Attributions
CC licensed content, Original
- Outcomes. Provided by: Lumen Learning License: CC BY: Attribution.
