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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Equation with one radical

Grade: 8-b Lesson: S2-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Discussion: Step1 Step2 Step3 Step4 Step5

Step	Type	Explanation	Answer
1	Problem	Solve the equation \$root(3)(2h - 9) - 1 = 2\$.
2	Step	Given equation	\$root(3)(2h - 9) - 1 = 2\$
3	Step	Add 1 to each side	\$root(3)(2h - 9) - 1 + 1 = 2 + 1\$
4	Hint	Cube each side to eliminate the radical	\$(root(3)(2h - 9) )^3 = 3^3\$
5	Step	Simplify	2h - 9 = 27
6	Clue	Add 9 to each side	2h = 36
7	Step	Divide each side by 2	h = 18
8	Step	Therefore, the solution is h = 18.
9	Choice.A	Substituting h = 12 leads to a cube root of 15. Without solving the cube root, we can’t confirm if it simplifies to a value that fits the equation (2 - 1)	h = 12
10	Choice.B	Substituting h = 14 results in a cube root of 19. Since cube roots of perfect cubes are integers, and 19 isn’t a perfect cube, h = 14 likely isn’t the solution	h = 14
11	Choice.C	Substituting h = 16 yields a cube root of 23. Prime numbers (like 23) don’t have perfect cube roots, making h = 16 a less probable solution	h = 16
12	Choice.D	Substituting h = 18 simplifies the radical to \$3\sqrt3\$. However, this directly contradicts the equation \$(3\sqrt(3) ≠ 2)\$, eliminating h = 18 as a solution	h = 18
13	Answer	Option	D
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the equation \$root(3)(2h - 9) - 1 = 2\$.

Step

Given equation

\$root(3)(2h - 9) - 1 = 2\$

Step

Add 1 to each side

\$root(3)(2h - 9) - 1 + 1 = 2 + 1\$

Hint

Cube each side to eliminate the radical

\$(root(3)(2h - 9) )^3 = 3^3\$

Step

Simplify

2h - 9 = 27

Clue

Add 9 to each side

2h = 36

Step

Divide each side by 2

h = 18

Step

Therefore, the solution is h = 18.

Choice.A

Substituting h = 12 leads to a cube root of 15. Without solving the cube root, we can’t confirm if it simplifies to a value that fits the equation (2 - 1)

h = 12

Choice.B

Substituting h = 14 results in a cube root of 19. Since cube roots of perfect cubes are integers, and 19 isn’t a perfect cube, h = 14 likely isn’t the solution

h = 14

Choice.C

Substituting h = 16 yields a cube root of 23. Prime numbers (like 23) don’t have perfect cube roots, making h = 16 a less probable solution

h = 16

Choice.D

Substituting h = 18 simplifies the radical to \$3\sqrt3\$. However, this directly contradicts the equation \$(3\sqrt(3) ≠ 2)\$, eliminating h = 18 as a solution

h = 18

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?

Discussion: Step1 Step2 Step3 Step4 Step5