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Lesson Example Discussion Quiz: Class Homework

Step-1

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 \$2\sqrt(k + 1) = 4\$.
2	Step	Write the original equation	\$2\sqrt(k + 1) = 4\$
3	Step	Divide each side by 2	\$2\sqrt(k + 1) = 4\$ \$\sqrt(k + 1) = 2\$
4	Hint	Square each side to eliminate the radical	\$(\sqrt(k + 1))^2 = 2^2\$
5	Step	Simplify	k + 1 = 4
6	Step	Subtract 1 from each side	k = 3
7	Step	Therefore, the solution is k = 3.
8	Choice.A	If we substitute k = 0 in the equation, we get: \$2\sqrt(0 + 1) = 4\$, which simplifies to \$2\sqrt1 = 4\$. This is not true because \$2\sqrt1 = 2\$ and not 4	k = 0
9	Choice.B	Substitute k = 1: \$2\sqrt(1 + 1) = 4\$, which becomes \$2\sqrt2 = 4\$. This is not true either. While \$\sqrt2\$ is approximately 1.41, \$2\sqrt2\$ is roughly 2.82 and not 4	k = 1
10	Choice.C	Substitute k = 2: \$2\sqrt(2 + 1) = 4\$, which simplifies to \$2\sqrt3 = 4\$. This is not a true statement. \$\sqrt3\$ is approximately 1.73, so \$2\sqrt3\$ is around 3.46 and not 4	k = 2
11	Choice.D	Substitute k = 3: \$2\sqrt(3 + 1) = 4\$, which becomes \$2\sqrt4 = 4\$. This is a true statement. \$\sqrt4\$ is 2, so \$2\sqrt4\$ is indeed 4	k = 3
12	Answer	Option	D
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the equation \$2\sqrt(k + 1) = 4\$.

Step

Write the original equation

\$2\sqrt(k + 1) = 4\$

Step

Divide each side by 2

\$2\sqrt(k + 1) = 4\$

\$\sqrt(k + 1) = 2\$

Hint

Square each side to eliminate the radical

\$(\sqrt(k + 1))^2 = 2^2\$

Step

Simplify

k + 1 = 4

Step

Subtract 1 from each side

k = 3

Step

Therefore, the solution is k = 3.

Choice.A

If we substitute k = 0 in the equation, we get: \$2\sqrt(0 + 1) = 4\$, which simplifies to \$2\sqrt1 = 4\$. This is not true because \$2\sqrt1 = 2\$ and not 4

k = 0

Choice.B

Substitute k = 1: \$2\sqrt(1 + 1) = 4\$, which becomes \$2\sqrt2 = 4\$. This is not true either. While \$\sqrt2\$ is approximately 1.41, \$2\sqrt2\$ is roughly 2.82 and not 4

k = 1

Choice.C

Substitute k = 2: \$2\sqrt(2 + 1) = 4\$, which simplifies to \$2\sqrt3 = 4\$. This is not a true statement. \$\sqrt3\$ is approximately 1.73, so \$2\sqrt3\$ is around 3.46 and not 4

k = 2

Choice.D

Substitute k = 3: \$2\sqrt(3 + 1) = 4\$, which becomes \$2\sqrt4 = 4\$. This is a true statement. \$\sqrt4\$ is 2, so \$2\sqrt4\$ is indeed 4

k = 3

Answer

Option

Sumup

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

Discussion: Step1 Step2 Step3 Step4 Step5