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

11 P Square & Cube Roots 8.EE.2 2,

Procedural Lesson

Grade 8 · Unit 2 · Lesson 11
MC: 8.EE. 2 

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Problem of the Day

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

Vocabulary Teacher Resources

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 =√^211 →푦푦= ±√ 11

Considerations:

Remind students that when a number is irrational

and cannot be simplified, find another number close

to the number described in the problem to

approximate the cube root.

Share with students that when taking the cube root,

a negative in the cube root does not mean the final

answer is irrational. This is because multiplying an

odd amount of negative numbers will result in a

negative answer.

Steps:

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.


8. Identify if the solution is rational or irrational.

Application of MPs:

MP2: How did you decide whether the solution is

rational?

I decided the solution is rational because ______.

MP6: Why do equations with a squared variable get ±

signs and cubed variables do not?

The squared variables get a ± because _______

but a cubed variable does not because _________.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

* ^ * * * *

cube root

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