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Five-Minute Check (over Lesson 6–6)

CCSS

Then/Now

New Vocabulary

Key Concept: Solving Radical Equations

Example 1:Solve Radical Equations

Example 2:Solve a Cube Root Equation

Example 3:Standardized Test Example: Solve a Radical Equation

Key Concept: Solving Radical Inequalities

Example 4:Solve a Radical Inequality

A.

B.

C.

D.

A.12

B.8

C.4

D.2

A.

B.

C.

D.

A.2w2

B.2w

C.w2

D.

A.

B.

C.5

D.10

The equation gives the approximate energy output y in kilocalories per day (kcal/day) for a reptile with a body mass m kilograms. The average mass of an alligator is 360 kilograms. Find the energy output of a reptile this size. Round your answer to the nearest tenth.

A.82.6 kcal/day

B.156.8 kcal/day

C.826.5 kcal/day

D.1568.1 kcal/day

Content Standards

A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

Mathematical Practices

4 Model with mathematics.

You solved polynomial equations.

- Solve equations containing radicals.

- Solve inequalities containing radicals.

- radical equation
- extraneous solution
- radical inequality

A.Solve .

Original equation

Add 1 to each side to isolate the radical.

Square each side to eliminate the radical.

Find the squares.

Add 2 to each side.

Solve Radical Equations

Original equation

?

Replace y with 38.

Simplify.

Solve Radical Equations

Check

Answer: The solution checks. The solution is 38.

B. Solve .

Original equation

Square each side.

Find the squares.

Isolate the radical.

Divide each side by –4.

Solve Radical Equations

Square each side.

Evaluate the squares.

Original equation

Check

Replace x with 16.

Simplify.

Evaluate the square roots.

Solve Radical Equations

Answer: The solution does not check, so there is no real solution.

A. Solve .

A.19

B.61

C.67

D.no real solution

B. Solve .

A.2

B.4

C.9

D.no real solution

In order to remove the power, or cube root, you must first isolate it and then raise each side of the equation to the third power.

Solve a Cube Root Equation

Original equation

Subtract 5 from each side.

Cube each side.

Evaluate the cubes.

Solve a Cube Root Equation

Subtract 1 from each side.

Divide each side by 3.

Check

Original equation

Replace y with –42.

Simplify.

The cube root of –125 is –5.

Add.

Answer: The solution is –42.

A.–14

B.4

C.13

D.26

Solve a Radical Equation

Am = –2

Bm = 0

Cm = 12

Dm = 14

Solve a Radical Equation

Original equation

Add 4 to each side.

Divide each side by 7.

Raise each side to the sixth power.

Evaluate each side.

Subtract 4 from each side.

Answer: The answer is C.

A.221

B.242

C.266

D.288

Solve a Radical Inequality

Since the radicand of a square root must be greater than or equal to zero, first solve 3x – 6 0 to identify the values of x for which the left side of the inequality is defined.

3x – 60

3x6

x2

Solve a Radical Inequality

Original inequality

Isolate the radical.

Eliminate the radical.

Add 6 to each side.

Divide each side by 3.

Answer: The solution is 2 x 5.

Test some x-values to confirm the solution. Let Use three test values: one less than 2, one between 2 and 5, and one greater than 5.

Solve a Radical Inequality

Check

Only the values in the interval 2 x 5 satisfy the inequality.

A.

B.

C.

D.