Exponents and Exponential Functions

Lesson 8

Objective

Simplify radical expressions.

Common Core Standards

Core Standards

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

Foundational Standards

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  • 8.EE.A.1

  • 8.EE.A.2

  • 8.NS.A.1

Criteria for Success

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  1. Rewrite radical expressions by evaluating any possible roots from inside the radical. For example, simplify a square root so that no perfect squares remain inside the square root. 
  2. Understand that $${\sqrt[n]{a^n}=a}$$.

Tips for Teachers

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Simplifying radicals will be a useful skill for when students compute with radicals in the upcoming lessons. It is helpful for students to be familiar with and to have readily in mind the perfect squares and cubes within 100.

Anchor Problems

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Problem 1

Determine which value is greater without calculating the value of the radical expression.

a.   $${11\sqrt3}$$ _____ $${13\sqrt3}$$

b.   $${\sqrt{72}}$$ _____ $${5\sqrt2}$$

c.   $${\sqrt{75}}$$ _____ $${2\sqrt{27}}$$

Guiding Questions

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Problem 2

Rewrite each expression as a radical with no perfect squares or cubes remaining inside the radical.

a.   $${\sqrt{32x^5y^2}}$$

b.   $${2\sqrt[3]{540m^7n^5}}$$

c.   $${(24x^2)^{1\over2}}$$

d.   $${(24x^2)^{1\over3}}$$

e.   $${(24x^2)^{2\over3}}$$

Guiding Questions

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Problem Set

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

Target Task

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Simplify each radical so there are no perfect squares or cubes remaining inside the radical.

a.   $${\sqrt{54x^8y^5}}$$

b.   $${\sqrt[3]{54x^8y^5}}$$