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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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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

B.

C.

D.

5-Minute Check 1

A. 12

B. 8

C. 4

D. 2

5-Minute Check 2

B.

C.

D.

5-Minute Check 3

A.2w2

B. 2w

C.w2

D.

5-Minute Check 4

B.

C.5

D. 10

5-Minute Check 5

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 output

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

Mathematical Practices

4 Model with mathematics.

CCSS

Then/Now

Vocabulary

Concept output

A. output Solve .

Original equation

Square each side to eliminate the radical.

Find the squares.

Example 1

Original equation output

?

Replace y with 38.

Simplify.

Check

Answer: The solution checks. The solution is 38.

Example 1

B. output Solve .

Original equation

Square each side.

Find the squares.

Divide each side by –4.

Example 1

Square each side. output

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. output Solve .

A. 19

B. 61

C. 67

D. no real solution

Example 1

B. output 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 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.

Example 2

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

B. 4

C. 13

D. 26

Example 2

Solve 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 3

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

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

B. 242

C. 266

D. 288

Example 3

Concept 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 4

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

Original inequality

Divide each side by 3.

Answer: The solution is 2  x  5.

Example 4

Test 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.

Check

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

Example 4

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

B.

C.

D.

Example 4

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