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Copyright © Swun Math Grade 8 Unit 2 Lesson 10 C TE

Cube Roots

Conceptual Lesson

Grade 8 · Unit 2 · Lesson 10
MC: 8 .EE. 2 

Problem of the Day

Objective: I will solve equations using cube roots.

Vocabulary Teacher Resources

Cube: the result of multiplying a base by itself

three times

2.1³ = 9.261

Perfect Cube: the result after multiplying an

integer three times by itself; also called a cubed

number

8 is a perfect cubed number

because 2 • 2 • 2 or 23 = 8

Cube Root: is a special value that, when used in

multiplication three times, gives the original

number

2 cubed is 8, so the cube root of 8 is 2

cube

2 8

cube root

√ and 푥푥^2 are inverse operations

√^3 and 푥푥^3 are inverse operations

Increase Exponentially:

Notice on the table

how the size increases

as the power increases.

This is called

increasing exponentially.

Negative Numbers:

53 = 5⋅ 5 ⋅5 = 125

(−5)^3 =− 5 ⋅− 5 ⋅−5 =− 125

 Multiplying an odd amount of negative numbers will

equal a negative answer.

Considerations:

Share with students that taking the cube root is

commonly used in equations involving volume.

Compare the concept of cubing and cube rooting as

opposites that cancel each other out.

When a number is irrational and cannot be simplified,

try to find another number close to the number

described in the problem statement to approximate

the cube root.

√^330 is between the 3 √ 27 and 3 √ 64

so the cube root of 30 is between 3 and 4

Discuss that when taking the cube root, a negative in

the cube root does not mean that the final answer is

irrational, because multiplying an odd amount of

negative numbers will result in a negative answer.

Steps:

1. Isolate the variable.


2. Take the cube root of both sides of the
   equation.


3. Identify the perfect cube root when possible.


4. Identify the value of the unknown.


5. Decide if the solution is rational or irrational.

Application of MPs:

MP2: How are squared values related to cubed

values?

They are related because _________________.

MP5: How does this problem compare to square

roots?

This problem is similar/different to square

roots by ___________________.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

* ^ ^ *

Number Squared Cubed

5 25 125

6 36 216

7 49 343

8 64 512

9 81 729

10 100 1000

11 121 1331

12 144 1728

13 169 2197

14 196 2744

15 225 3375

Student Journal Pages

94 - 97