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

Homework

Unit 2 · Lesson 10 : Cube Roots

Objective: I will solve equations using cube roots.

(^)
Vocabulary Steps
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
− 53 =− 5 ⋅− 5 ⋅−5 =− 125

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.

Remember:

 Multiplying an odd number of negative

numbers will result in a negative product.

Example # 1 Example # 2

Directions: Solve. Determine if the solution is rational or irrational.

푚푚^3 = 8

Solution:

Step 1: 푚푚^3 = 8

Step 2: √푚푚^33 =^3 √ 8

Step 3: (^) √^3 푚푚⋅푚푚⋅푚푚= √^32 ⋅ 2 ⋅ 2
Step 4: 푚푚= 2
Step 5: The solution is 푚푚= 2 ; a rational number.
푛푛^3 = 13
Solution:
Step 1: 푛푛^3 = 13
Step 2: 3 √푛푛^3 =^3 √ 13
Step 3: (^) √^3 푛푛⋅푛푛⋅푛푛=√^313 (no perfect cube can be found)
Step 4: 푛푛=√^313
Step 5: The solution is √^313 ; irrational.
Name:
Date:
Number Squared Cubed
5 25 125
6 36 216
7 49 343
8 64 729
9 81 729
10 100 1000
11 121 1331
12 144 1728
13 169 2197
14 196 2744
15 225 3375