Splash Screen

Five-Minute Check (over Lesson 6–3) CCSS Then/Now New Vocabulary Key Concept: Definition of nth Root Key Concept: Real nth Roots Example 1: Find Roots Example 2: Simplify Using Absolute Value Example 3: Real-World Example: Approximate Radicals Lesson Menu

A. B. C. D. D = {x | x ≤ –2}, R = {y | y ≥ 0} 5-Minute Check 1

A. B. C. D. D = {x | x ≤ –2}, R = {y | y ≥ 0} 5-Minute Check 1

A. B. C. D. 5-Minute Check 2

A. B. C. D. 5-Minute Check 2

A. B. C. D. 5-Minute Check 3

A. B. C. D. 5-Minute Check 3

A. B. C. D. 5-Minute Check 4

A. B. C. D. 5-Minute Check 4

C. D. A. B. 5-Minute Check 5

C. D. A. B. 5-Minute Check 5

The point (3, 6) lies on the graph of Which ordered pair lies on the graph of B. C. (2, –2) D. (–2, 2) 5-Minute Check 6

The point (3, 6) lies on the graph of Which ordered pair lies on the graph of B. C. (2, –2) D. (–2, 2) 5-Minute Check 6

Mathematical Practices 6 Attend to precision. Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 6 Attend to precision. CCSS

You worked with square root functions. Simplify radicals. Use a calculator to approximate radicals. Then/Now

nth root radical sign index radicand principal root Vocabulary

Concept

Concept

Find Roots = ±4x4 Answer: Example 1

Answer: The square roots of 16x8 are ±4x4. Find Roots = ±4x4 Answer: The square roots of 16x8 are ±4x4. Example 1

Find Roots Answer: Example 1

Find Roots Answer: The opposite of the principal square root of (q3 + 5)4 is –(q3 + 5)2. Example 1

Find Roots Answer: Example 1

Find Roots Answer: Example 1

Find Roots Answer: Example 1

Find Roots Answer: Example 1

A. Simplify . A. ±3x6 B. ±3x4 C. 3x4 D. ±3x2 Example 1

A. Simplify . A. ±3x6 B. ±3x4 C. 3x4 D. ±3x2 Example 1

B. Simplify . A. –(a3 + 2)4 B. –(a3 + 2)8 C. (a3 + 2)4 D. (a + 2)4 Example 1

B. Simplify . A. –(a3 + 2)4 B. –(a3 + 2)8 C. (a3 + 2)4 D. (a + 2)4 Example 1

C. Simplify . A. 2xy2 B. ±2xy2 C. 2y5 D. 2xy Example 1

C. Simplify . A. 2xy2 B. ±2xy2 C. 2y5 D. 2xy Example 1

Simplify Using Absolute Value Note that t is a sixth root of t 6. The index is even, so the principal root is nonnegative. Since t could be negative, you must take the absolute value of t to identify the principal root. Answer: Example 2

Simplify Using Absolute Value Note that t is a sixth root of t 6. The index is even, so the principal root is nonnegative. Since t could be negative, you must take the absolute value of t to identify the principal root. Answer: Example 2

Since the index is odd, you do not need absolute value. Simplify Using Absolute Value Since the index is odd, you do not need absolute value. Answer: Example 2

Since the index is odd, you do not need absolute value. Simplify Using Absolute Value Since the index is odd, you do not need absolute value. Answer: Example 2

A. Simplify . A. x B. –x C. |x| D. 1 Example 2

A. Simplify . A. x B. –x C. |x| D. 1 Example 2

B. Simplify . A. |3(x + 2)3| B. 3(x + 2)3 C. |3(x + 2)6| D. 3(x + 2)6 Example 2

B. Simplify . A. |3(x + 2)3| B. 3(x + 2)3 C. |3(x + 2)6| D. 3(x + 2)6 Example 2

Understand You are given the value for k. Approximate Radicals A. SPACE Designers must create satellites that can resist damage from being struck by small particles of dust and rocks. A study showed that the diameter in millimeters d of the hole created in a solar cell by a dust particle traveling with energy k in joules is about Estimate the diameter of a hole created by a particle traveling with energy 3.5 joules. Understand You are given the value for k. Plan Substitute the value for k into the formula. Use a calculator to evaluate. Example 3A

Solve Original formula Approximate Radicals Solve Original formula k = 3.5 Use a calculator. Answer: Example 3A

Solve Original formula Approximate Radicals Solve Original formula k = 3.5 Use a calculator. Answer: The hole created by a particle traveling with energy of 3.5 joules will have a diameter of approximately 1.237 millimeters. Example 3A

Check Original equation Approximate Radicals Check Original equation Add 0.169 to each side. Divide both sides by 0.926. Cube both sides. Simplify. Example 3A

Approximate Radicals B. SPACE Designers must create satellites that can resist damage from being struck by small particles of dust and rocks. A study showed that the diameter in millimeters d of the hole created in a solar cell by a dust particle traveling with energy k in joules is about If a hole has diameter of 2.5 millimeters, estimate the energy with which the particle that made the hole was traveling. Example 3B

Solve Original formula Approximate Radicals Solve Original formula d = 2.5 Use a calculator. Answer: Example 3B

Solve Original formula Approximate Radicals Solve Original formula d = 2.5 Use a calculator. Answer: The hole with a diameter of 2.5 millimeters was created by a particle traveling with energy of 23.9 joules. Example 3B

A. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. Find the value of T for a 2-foot-long pendulum. A. about 0.25 second B. about 1.57 seconds C. about 12.57 seconds D. about 25.13 seconds Example 3A

A. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. Find the value of T for a 2-foot-long pendulum. A. about 0.25 second B. about 1.57 seconds C. about 12.57 seconds D. about 25.13 seconds Example 3A

B. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. How long is the pendulum if it takes 5 seconds to swing back and forth? A. about 2.5 feet B. about 10 feet C. about 20.3 feet D. about 25.5 feet Example 3B

B. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. How long is the pendulum if it takes 5 seconds to swing back and forth? A. about 2.5 feet B. about 10 feet C. about 20.3 feet D. about 25.5 feet Example 3B

End of the Lesson