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Lesson Example Discussion Quiz: Class Homework

Step-5

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 following radical equation: \$ root(4) (11 - 5s) = 1\$.
2	Step	The given equation	\$ root(4) (11 - 5s) = 1\$
3	Hint	Remove the fourth root by raising both sides to the fourth power:	\$ (root(4) (11 - 5s))^4 = 1^4\$ 11 - 5s = 1
4	Step	Solve for s:	⇒ - 5s = 1 - 11 ⇒ - 5s = - 10 \$s = - \cancel(10)^2 / -\cancel(5)\$ ⇒ s = 2
5	Step	Therefore, the solution to the equation \$ root(4) (11 - 5s) = 1\$ is 2.
6	Choice.A	s = 5 is not correct because it does not yield a real number when substituted back into the original equation	s = 5
7	Choice.B	s = 2 is correct because it satisfies the original equation \$ root(4) (11 - 5s) = 1\$	s = 2
8	Choice.C	s = −5 is not correct because substituting s = − 5 into the equation gives: \$root(4) ( 11- 5 - 5) = root(4) ( 11 + 25) = root(4) (36)\$. Since \$root(4) (36) = 2\$ not 1 s = − 5 does not satisfy the equation	s = -5
9	Choice.D	This equation is not true because \$root(4) (21)\$ does not equal 1. Therefore, s = − 2 is not a correct solution	s = -2
10	Answer	Option	B
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the following radical equation:
\$ root(4) (11 - 5s) = 1\$.

Step

The given equation

\$ root(4) (11 - 5s) = 1\$

Hint

Remove the fourth root by raising both sides to the fourth power:

\$ (root(4) (11 - 5s))^4 = 1^4\$

11 - 5s = 1

Step

Solve for s:

⇒ - 5s = 1 - 11

⇒ - 5s = - 10

\$s = - \cancel(10)^2 / -\cancel(5)\$

⇒ s = 2

Step

Therefore, the solution to the equation \$ root(4) (11 - 5s) = 1\$ is 2.

Choice.A

s = 5 is not correct because it does not yield a real number when substituted back into the original equation

s = 5

Choice.B

s = 2 is correct because it satisfies the original equation \$ root(4) (11 - 5s) = 1\$

s = 2

Choice.C

s = −5 is not correct because substituting s = − 5 into the equation gives: \$root(4) ( 11- 5 - 5) = root(4) ( 11 + 25) = root(4) (36)\$. Since \$root(4) (36) = 2\$ not 1 s = − 5 does not satisfy the equation

s = -5

Choice.D

This equation is not true because \$root(4) (21)\$ does not equal 1. Therefore, s = − 2 is not a correct solution

s = -2

Answer

Option

Sumup

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

Discussion: Step1 Step2 Step3 Step4 Step5