Unlock the Cube: Finding Cube Roots of Negative Numbers

Algebra 1 Grades High School 4:18 Video
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Lesson Description

Learn how to find the cube root of negative numbers using prime factorization, as demonstrated by Khan Academy. This lesson explores the relationship between a number and its cube root and provides a step-by-step method for solving.

Video Resource

Cube root of a negative number (example) | Pre-Algebra | Khan Academy

Khan Academy

Duration: 4:18
Watch on YouTube

Key Concepts

  • Cube Root Definition
  • Prime Factorization
  • Properties of Negative Numbers

Learning Objectives

  • Students will be able to define cube root and explain its relationship to cubing a number.
  • Students will be able to find the cube root of a negative number using prime factorization.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of square roots and perfect squares. Transition to cube roots by asking what number, when multiplied by itself three times, results in a given number. Introduce the idea that cube roots can be negative, unlike square roots.
  • Khan Academy Video (10 mins)
    Play the Khan Academy video 'Cube root of a negative number (example)'. Instruct students to take notes on the steps involved in finding the cube root of -512.
  • Guided Practice (15 mins)
    Work through a similar example on the board, such as finding the cube root of -216. Emphasize the steps: 1) Separate the negative sign, 2) Prime factorize the number, 3) Group the prime factors into sets of three, 4) Find the cube root of the positive number, and 5) Apply the negative sign.
  • Independent Practice (15 mins)
    Assign students practice problems to solve individually. Examples: cube root of -125, cube root of -1000, cube root of -8.
  • Wrap-up (5 mins)
    Review the key concepts and answer any remaining questions. Briefly introduce the concept of simplifying cube roots with non-perfect cube numbers.

Interactive Exercises

  • Prime Factorization Race
    Divide the class into groups. Give each group a negative number and have them race to find the prime factorization and the cube root. The first group to correctly solve the problem wins.
  • Online Cube Root Calculator
    Use an online cube root calculator to verify answers and explore more complex cube roots.

Discussion Questions

  • How does finding the cube root differ from finding the square root?
  • Why can we take the cube root of a negative number, but not the square root (in the realm of real numbers)?
  • Can you think of real-world situations where cube roots might be used?

Skills Developed

  • Prime Factorization
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

What is the cube root of -8?

Correct Answer: -2

Question 2:

Which of the following is the prime factorization of 512?

Correct Answer: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Question 3:

What does it mean to find the cube root of a number?

Correct Answer: Finding a number that, when multiplied by itself twice, equals the original number.

Question 4:

What is the cube root of -1?

Correct Answer: -1

Question 5:

What is the first step in finding the cube root of a negative number using prime factorization?

Correct Answer: Separate the negative sign

Question 6:

What is the cube root of -27?

Correct Answer: -3

Question 7:

What is the cube root of -64?

Correct Answer: -4

Question 8:

What is the cube root of -125?

Correct Answer: -5

Question 9:

What is the cube root of -1000?

Correct Answer: -10

Question 10:

The cube root of a negative number will always be:

Correct Answer: Negative

Fill in the Blank Questions

Question 1:

The cube root of -512 is ______.

Correct Answer: -8

Question 2:

______ factorization is a method used to find the cube root of a number.

Correct Answer: Prime

Question 3:

The cube root of -1 is ______.

Correct Answer: -1

Question 4:

The opposite operation of finding a cube root is raising a number to the third ______.

Correct Answer: power

Question 5:

The cube root of -216 is ______.

Correct Answer: -6

Question 6:

The cube root of -343 is ______.

Correct Answer: -7

Question 7:

The cube root of -1728 is ______.

Correct Answer: -12

Question 8:

The cube root of -2744 is ______.

Correct Answer: -14

Question 9:

The cube root of -4096 is ______.

Correct Answer: -16

Question 10:

In order to find the cube root of a number, we need to find a number that, when multiplied by itself ______ times, yields the original number.

Correct Answer: three

Educational Standards

A1.N.1:[Standard] Extend the understanding of exponents to include square roots and cube roots. A1.N.1.1:[Objective] Write square roots and cube roots of constants and monomial algebraic expressions in simplest radical form. A1.A.3.4:[Objective] Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.

Teaching Materials

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