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## Splash Screen

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**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**A.**B. C. D. 5-Minute Check 5**A.**B. C. D. 5-Minute Check 5**The point (3, 6) lies on the graph of Which ordered pair**lies on the graph of A. 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 A. B. C.(2, –2) D.(–2, 2) 5-Minute Check 6**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**Find Roots**= ±4x4 Answer: Example 1**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**Answer:**Find Roots Example 1**Find Roots**Answer: Example 1**Answer:**Find Roots 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 t6. 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**Answer:**Simplify Using Absolute Value Note that t is a sixth root of t6. 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. Example 2**Simplify Using Absolute Value**Since the index is odd, you do not need absolute value. Answer: Example 2**Answer:**Simplify Using Absolute Value Since the index is odd, you do not need absolute value. 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**A. SPACEDesigners 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. Approximate Radicals 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 k = 3.5 Use a calculator. Answer: Example 3A**Solve Original formula**Approximate Radicals 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 Add 0.169 to each side. Divide both sides by 0.926. Cube both sides. Simplify. Example 3A**B. SPACEDesigners 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. Approximate Radicals Example 3B**Solve Original formula**Approximate Radicals d = 2.5 Use a calculator. Answer: Example 3B**Solve Original formula**Approximate Radicals 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