G8

Input/Model

(Teacher Presents)

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.
Talking points:

Begin by identifying the unknown.

Notice the exponent indicates it is a cubic problem.

To undo this power, take the cubic root of both sides of the equation.

Since a cubed number and the cubed root of a number are inverse operations, they “undo” or cancel each
other out.

Solve using steps.

푛푛^3 = 13

Solution: Step 1: 푛푛^3 = 13

Step 2: √푛푛^33 =√^313

Step 3: (^) √^3 푛푛⋅푛푛⋅푛푛=√^313 (no perfect cube can be found)
Step 4: 푛푛=^3 √ 13
Step 5: The solution is (^3) √ 13 ; irrational.

Input/Model