- 109 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Splash Screen' - belle-bradshaw

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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

Lesson MenuThe 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 6Content Standards output

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

Mathematical Practices

4 Model with mathematics.

CCSSYou solved polynomial equations. output

- Solve equations containing radicals.

- Solve inequalities containing radicals.

- radical equation output
- extraneous solution
- radical inequality

Concept output

A. output 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

Example 1Original equation output

?

Replace y with 38.

Simplify.

Solve Radical Equations

Check

Answer: The solution checks. The solution is 38.

Example 1B. output Solve .

Original equation

Square each side.

Find the squares.

Isolate the radical.

Divide each side by –4.

Solve Radical Equations

Example 1Square each side. output

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.

Example 1In 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 2Solve a Cube Root Equation first isolate it and then raise each side of the equation to the third power.

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.

Example 2A. first isolate it and then raise each side of the equation to the third power. –14

B. 4

C. 13

D. 26

Example 2Solve a Radical Equation first isolate it and then raise each side of the equation to the third power.

Am = –2

Bm = 0

Cm = 12

Dm = 14

Example 3Solve a Radical Equation first isolate it and then raise each side of the equation to the third power.

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.

Example 3A. first isolate it and then raise each side of the equation to the third power. 221

B. 242

C. 266

D. 288

Example 3Concept first isolate it and then raise each side of the equation to the third power.

Solve a Radical Inequality first isolate it and then raise each side of the equation to the third power.

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 4Solve a Radical Inequality first isolate it and then raise each side of the equation to the third power.

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.

Example 4Test some first isolate it and then raise each side of the equation to the third power.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.

Example 4End of the Lesson first isolate it and then raise each side of the equation to the third power.

Download Presentation

Connecting to Server..