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Splash Screen. 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

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Presentation Transcript
Five-Minute Check (over Lesson 6–6)

CCSS

Then/Now

New Vocabulary

Example 2: Solve a Cube Root Equation

Example 3: Standardized Test Example: Solve a Radical Equation

Example 4: Solve a Radical Inequality

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

5-Minute Check 6
Content Standards

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

Mathematical Practices

4 Model with mathematics.

CCSS
You solved polynomial equations.
Then/Now
• extraneous solution
Vocabulary
A.Solve .

Original equation

Square each side to eliminate the radical.

Find the squares.

Example 1
Original equation

?

Replace y with 38.

Simplify.

Check

Answer: The solution checks. The solution is 38.

Example 1
B. Solve .

Original equation

Square each side.

Find the squares.

Divide each side by –4.

Example 1
Square each side.

Evaluate the squares.

Original equation

Check

Replace x with 16.

Simplify.

Evaluate the square roots.

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

Example 1
A. Solve .

A. 19

B. 61

C. 67

D. no real solution

Example 1
B. Solve .

A. 2

B. 4

C. 9

D. no real solution

Example 1
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.

Example 2
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.

Example 2
A. –14

B. 4

C. 13

D. 26

Example 2

Am = –2

Bm = 0

Cm = 12

Dm = 14

Example 3

Original equation

Divide each side by 7.

Raise each side to the sixth power.

Evaluate each side.

Subtract 4 from each side.

Example 3
A. 221

B. 242

C. 266

D. 288

Example 3

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

Example 4

Original inequality

Divide each side by 3.

Answer: The solution is 2  x  5.

Example 4
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.