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Copyright © Swun Math Grade 8 Unit 2 Lesson 11 P TE

Homework

Unit 2 · Lesson 11: Square & Cube Roots

Objective: I will solve equations using square roots and cubic roots.

Vocabulary Steps:

Square Root: the square root

of a number is a value that,

when multiplied by itself,

gives the number

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

Inverse Operations:

� and 푥푥^2 are inverse operations

�^3  and 푥푥^3 are inverse operations

Rational Solution: solutions to equations that are

integers or fractions

푦푦^2 = 9 → �푦푦^22 =√^29 = 3

Irrational Solution: solutions to equations that

cannot be written as a simple fraction

푦푦^2 = 11 → �푦푦^22 =^2 √ 11 →푦푦= ±√ 11

1. Isolate the variable.


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


3. Identify the perfect square when possible.


4. Identify the 2 possible values for the
   unknown.


5. Identify if the solution is rational or
   irrational.
   OR


6. Identify the perfect cube root when possible.


7. Identify the value of the unknown.
   Identify if the solution is rational or
   irrational.

Examples

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

푗푗^2 = 36

Solution:

Step 1: 푗푗^2 = 36

Step 2: �푗푗^2 =√ 36

Step 3: �푗푗⋅푗푗=√ 6 ⋅ 6

Step 4  Solution 1: 푗푗= 6

Solution 2: 푗푗=− 6

Step 5: The solution is 푗푗= ±6, a rational number.

ℎ^3 = 64

Solution:

Step 1: ℎ^3 = 64

Step 2: 3 √ℎ^3 =^3 √ 64

Step 3: 3 √ℎ⋅ℎ⋅ℎ=√^34 ⋅ 4 ⋅ 4

Step 4: ℎ= 4

Step 5: The solution is ℎ= 4, a rational number.

Name: ___

Date: ___

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

cube root