Rational and Radical Functions

Lesson 5

Math

Unit 4

11th Grade

Lesson 5 of 18

Objective


Write radical and rational exponent expressions in equivalent forms.

Common Core Standards


Core Standards

  • N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Foundational Standards

  • 8.EE.A.1

Criteria for Success


  1. Write rational exponents as radicals and radicals as rational exponents.
  2. Rationalize the denominator of a radical expression. 
  3. Describe the equivalence of the expression with the rationalized denominator and those without a rationalized denominator. 
  4. Simplify expressions with rational exponents. 

Tips for Teachers


Students will likely need to review exponent rules in conjunction with rational exponents. They have not worked extensively with this concept since Algebra 1. 

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Anchor Problems


Problem 1

For $${x>0}$$, the expression $${3(\sqrt{x})^5\over(\sqrt[3]{x})^2}$$ can be written in the form $${3x^a}$$, where a is a fraction. 
What is the value of $$a$$

Guiding Questions

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Problem 2

Write each expression so that the fraction has a rational expression in the denominator. 

a.   $${x-9\over{\sqrt{x-9}}}$$

 

b.   $${x-9\over{\sqrt{x}+3}}$$

Guiding Questions

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References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 28Example 2

Algebra II > Module 1 > Topic C > Lesson 28 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Target Task


Problem 1

Rationalize the denominator. 

$${x^2-16\over{\sqrt{x}-2}}$$

Problem 2

Rewrite the following expression with a radical, in simplest form. 

$${8x^2\over2x^{-5\over2}}$$

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 4

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Lesson 6

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to Rational and Radical Functions and Expressions

Topic B: Features of Rational Functions and Graphing Rational Functions

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

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