Curriculum / Math / 9th Grade / Unit 6: Exponents and Exponential Functions / Lesson 8
Math
Unit 6
9th Grade
Lesson 8 of 22
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Simplify radical expressions.
The core standards covered in this lesson
N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.
The foundational standards covered in this lesson
8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.
8.EE.A.2 — Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
8.NS.A.1 — Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Determine which value is greater without calculating the value of the radical expression.
a. $${11\sqrt3}$$ _____ $${13\sqrt3}$$
b. $${\sqrt{72}}$$ _____ $${5\sqrt2}$$
c. $${\sqrt{75}}$$ _____ $${2\sqrt{27}}$$
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. $${(24x^2)^{2\over3}}$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Simplify each radical so there are no perfect squares or cubes remaining inside the radical.
a.  $${\sqrt{54x^8y^5}}$$
b.  $${\sqrt[3]{54x^8y^5}}$$
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.
Lesson 7
Lesson 9
Topic A: Exponent Rules, Expressions, and Radicals
Use exponent rules to analyze and rewrite expressions with non-negative exponents.
8.EE.A.1
Add and subtract polynomial expressions using properties of operations.
A.APR.A.1
Multiply polynomials using properties of exponents and properties of operations.
Solve mathematical applications of exponential expressions.
Use negative exponent rules to analyze and rewrite exponential expressions.
8.EE.A.1 A.SSE.A.2
Define rational exponents and convert between rational exponents and roots.
N.RN.A.1 N.RN.A.2
Write equivalent radical and rational exponent expressions. Identify quantities as rational or irrational.
N.RN.B.3
N.RN.A.2
Multiply and divide rational exponent expressions and radical expressions.
N.RN.A.2 N.RN.B.3
Add and subtract rational exponent expressions and radical expressions.
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Topic B: Arithmetic and Geometric Sequences
Describe and analyze sequences given their recursive formulas.
F.BF.A.2 F.IF.A.2 F.IF.A.3
Write recursive formulas for sequences, including the Fibonacci sequence.
Define arithmetic and geometric sequences, and identify common ratios and common differences in sequences.
F.BF.A.2 F.LE.A.2
Write explicit rules for arithmetic sequences and translate between explicit and recursive formulas.
F.BF.A.2 F.IF.A.3 F.LE.A.2
Write explicit rules for geometric sequences and translate between explicit and recursive formulas.
Topic C: Exponential Growth and Decay
Compare rates of change in linear and exponential functions shown as equations, graphs, and situations.
A.SSE.A.1 F.IF.C.9 F.LE.A.1 F.LE.A.3
Write linear and exponential models for real-world and mathematical problems.
A.SSE.A.1 F.LE.A.1 F.LE.A.2 F.LE.B.5
Graph exponential growth functions and write exponential growth functions from graphs.
F.BF.B.3 F.IF.C.7.E
Write exponential growth functions to model financial applications, including compound interest.
F.IF.C.8.B F.LE.A.2 F.LE.B.5
Write, graph, and evaluate exponential decay functions.
F.BF.B.3 F.IF.C.7.E F.IF.C.8.B F.LE.A.1.C
Identify features of exponential decay in real-world problems.
F.IF.C.8.B F.LE.A.1.C
Solve exponential growth and exponential decay application problems.
F.IF.C.8.B F.LE.A.1 F.LE.A.2
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