Exponents and Exponential Functions

Lesson 10

Math

Unit 6

9th Grade

Lesson 10 of 22

Objective


Add and subtract rational exponent expressions and radical expressions.

Common Core Standards


Core Standards

  • N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.
  • N.RN.B.3 — Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Foundational Standards

  • 8.EE.A.1
  • 8.EE.A.2
  • 8.NS.A.1

Criteria for Success


  1. Understand that $${x\sqrt[n]{a}+y\sqrt[n]{a}=(x+y)\sqrt[n]{a}}$$.
  2. Understand that radicals with different indices or radicands cannot be combined. 
  3. Apply the properties of exponents and properties of operations to add and subtract rational exponent and radical expressions.
  4. Understand that a rational number added to or subtracted from a rational number is rational, and a rational number added to or subtracted from an irrational number is irrational.
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Anchor Problems


Problem 1

The statement below is incorrect. Explain why it is incorrect and then correct the statement.

$${\sqrt9+\sqrt9=\sqrt{18}}$$

Which statements below are true? Select all that apply.

a.   $${2\sqrt3+\sqrt3=3\sqrt3}$$

b.   $${10\sqrt5-5\sqrt5=5}$$

c.   $${\sqrt2+\sqrt[3]{2}=2\sqrt2}$$

d.   $${4\sqrt8-3\sqrt8=\sqrt8}$$

e.   $${5\sqrt{8}-2\sqrt{6}=3\sqrt2}$$

f.   $${8\sqrt[n]{x}-6\sqrt[n]{x}=2\sqrt[n]{x}}$$

Guiding Questions

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Problem 2

Compute and simplify.

a.   $${\sqrt{48}+2\sqrt{27}-3\sqrt{12}}$$

b.   $${-5\sqrt{20}-\sqrt{72}+\sqrt{125}}$$

c.   $${(\sqrt[3]{16}+\sqrt[3]{54})^3}$$

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Compute and simplify.

a.   $${\sqrt{8a}-\sqrt{32a}}$$

b.   $${8\sqrt{18}-4\sqrt{8}-\sqrt{24}}$$

c.   $${\sqrt{3}(2\sqrt{18}+\sqrt{32})}$$

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 9

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Lesson 11

Lesson Map

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

Topic A: Exponent Rules, Expressions, and Radicals

Topic B: Arithmetic and Geometric Sequences

Topic C: Exponential Growth and Decay

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