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Lesson Example Discussion Quiz: Class Homework

Step-2

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 for the variable in the following radical equations: \$ root(3) ( 5 - y) = - 8\$
2	Step	The given equation is	\$ root(3) ( 5 - y) = - 8\$
3	Hint	Cube both sides to eliminate the cube root and then simplify:	\$(root(3)(5 - y))^3 = (- 8) ^3\$ 5 - y = - 512
4	Step	Solve for y:	⇒ - y = - 512 - 5 ⇒ - y = - 517
5	Clue	Multiply both sides by -1 to solve for y:	\$ -1 times - y = - 517 times - 1\$ y = 517
6	Step	Therefore, the solution to the equation \$ root(3) ( 5 - y) = - 8\$ is 517.
7	Choice.A	Substituting y = 517 satisfies the original equation, confirming its accuracy	y = 517
8	Choice.B	Option B is wrong because y = 571 does not satisfy the equation. Plugging y = 571 into the original equation	y = 571
9	Choice.C	Option C, which states y = −517, is incorrect because the steps above clearly show that the correct value of y is 517, not -517	y = -517
10	Choice.D	Substituting y = − 571 does not satisfy the original equation, confirming that Option D is incorrect	y = -571
11	Answer	Option	A
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve for the variable in the following radical equations:
\$ root(3) ( 5 - y) = - 8\$

Step

The given equation is

\$ root(3) ( 5 - y) = - 8\$

Hint

Cube both sides to eliminate the cube root and then simplify:

\$(root(3)(5 - y))^3 = (- 8) ^3\$

5 - y = - 512

Step

Solve for y:

⇒ - y = - 512 - 5

⇒ - y = - 517

Clue

Multiply both sides by -1 to solve for y:

\$ -1 times - y = - 517 times - 1\$

y = 517

Step

Therefore, the solution to the equation \$ root(3) ( 5 - y) = - 8\$ is 517.

Choice.A

Substituting y = 517 satisfies the original equation, confirming its accuracy

y = 517

Choice.B

Option B is wrong because y = 571 does not satisfy the equation. Plugging y = 571 into the original equation

y = 571

Choice.C

Option C, which states y = −517, is incorrect because the steps above clearly show that the correct value of y is 517, not -517

y = -517

Choice.D

Substituting y = − 571 does not satisfy the original equation, confirming that Option D is incorrect

y = -571

Answer

Option

Sumup

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

Discussion: Step1 Step2 Step3 Step4 Step5