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

Over Lesson 6–6

A.

B.

C.

D.

Over Lesson 6–6

A. 12

B. 8

C. 4

D. 2

Over Lesson 6–6

A.

B.

C.

D.

Over Lesson 6–6

A. 2w

2

B. 2w

C. w

2

D.

Over Lesson 6–6

A.

B.

C. 5

D. 10

Over Lesson 6–6

A. 82.6 kcal/day

B. 156.8 kcal/day

C. 826.5 kcal/day

D. 1568.1 kcal/day

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.

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

Solve Radical Equations

A. Solve .

Add 2 to each side.

Find the squares.

Square each side to eliminate the radical.

Add 1 to each side to isolate the radical.

Original equation

Solve Radical Equations

Original equation

Answer: The solution checks. The solution is 38.

Check

Simplify.

Replace y with 38.?

Solve Radical Equations

B. Solve .

Divide each side by –4.

Isolate the radical.

Find the squares.

Square each side.

Original equation

Solve Radical Equations

Square each side.

Evaluate the squares.

Replace x with 16.

Simplify.

Original equationCheck

Evaluate the square roots.

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

A. 19

B. 61

C. 67

D. no real solution

A. Solve .

B. Solve .

A. 2

B. 4

C. 9

D. no real solution

Solve a Cube Root Equation

Original equation

Subtract 5 from each side.

Cube each side.

Evaluate the cubes.

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

Answer: The solution is –42.

Subtract 1 from each side.

Divide each side by 3.

Original equation

Replace y with –42.

Simplify.

The cube root of –125 is –5.Add.

Check

A. –14

B. 4

C. 13

D. 26

A m = –2

B m = 0

C m = 12

D m = 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.

Solve a Radical Equation

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 – 6 0

3x 6

x 2

Solve a Radical Inequality

Answer: The solution is 2 x 5.

Original inequality

Isolate the radical.

Eliminate the radical.

Add 6 to each side.

Divide each side by 3.

Solve a Radical Inequality

Check

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

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.

A.

B.

C.

D.