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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Equation with two radicals

Grade: 8-b Lesson: S2-L4

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	Simplify the following two radicals \$root(3) (- 4p +8) = root(3) (3(7) + 5p - 9)\$.
2	Step	The given two radicals	\$root(3) (- 4p + 8) = root(3) (3(7) + 5p - 9)\$
3	Step	First simplify the expression inside the cube roots: ( right-hand side)	\$ 3(7) + 5p -9 \$ 21 + 5p - 9 12 + 5p
4	Step	Now the equation becomes:	\$root(3) (- 4p + 8) = root(3) (12+ 5p )\$
5	Hint	Since the cube roots of two expressions are equal, the expressions themselves must be equal:	-4p + 8 = 12 + 5p
6	Step	Isolate p by moving all terms involving p to one side and the constants to the other:	-4p - 5p = 12 - 8 ⇒ -9p = 4 \$p = - 4/9\$
7	Step	Therefore, the solution to the two radicals equation is \$ p = -4/9\$.
8	Choice.A	The sign is incorrect: the correct solution should include a negative sign	\$p = 4/9\$
9	Choice.B	It is incorrect because it does not satisfy the equation derived from setting the cube roots equal	\$p = - 9/4\$
10	Choice.C	Option C is correct it satisfies the original radicals equation	\$p = - 4/9\$
11	Choice.D	Wrong: It does not satisfy the equation derived from setting the cube roots equal	\$p = 9/4\$
12	Answer	Option	C
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Simplify the following two radicals \$root(3) (- 4p +8) = root(3) (3(7) + 5p - 9)\$.

Step

The given two radicals

\$root(3) (- 4p + 8) = root(3) (3(7) + 5p - 9)\$

Step

First simplify the expression inside the cube roots: ( right-hand side)

\$ 3(7) + 5p -9 \$

21 + 5p - 9

12 + 5p

Step

Now the equation becomes:

\$root(3) (- 4p + 8) = root(3) (12+ 5p )\$

Hint

Since the cube roots of two expressions are equal, the expressions themselves must be equal:

-4p + 8 = 12 + 5p

Step

Isolate p by moving all terms involving p to one side and the constants to the other:

-4p - 5p = 12 - 8

⇒ -9p = 4

\$p = - 4/9\$

Step

Therefore, the solution to the two radicals equation is \$ p = -4/9\$.

Choice.A

The sign is incorrect: the correct solution should include a negative sign

\$p = 4/9\$

Choice.B

It is incorrect because it does not satisfy the equation derived from setting the cube roots equal

\$p = - 9/4\$

Choice.C

Option C is correct it satisfies the original radicals equation

\$p = - 4/9\$

Choice.D

Wrong: It does not satisfy the equation derived from setting the cube roots equal

\$p = 9/4\$

Answer

Option

Sumup

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

Discussion: Step1 Step2 Step3 Step4 Step5