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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
Over Lesson 6–3
A.
B.
C.
D. D = {x | x ≤ –2}, R = {y | y ≥ 0}
Over Lesson 6–3
A.
B.
C.
D.
Over Lesson 6–3
A.
B.
C.
D.
Over Lesson 6–3
A.
B.
C.
D.
Over Lesson 6–3
C.
D.
A.
B.
Over Lesson 6–3
A.
B.
C. (2, –2)
D. (–2, 2)
The point (3, 6) lies on the graph of Which ordered pair lies on the graph of
Content Standards
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Mathematical Practices
6 Attend to precision.
You worked with square root functions.
• Simplify radicals.
• Use a calculator to approximate radicals.
• nth root
• radical sign
• index
• radicand
• principal root
Find Roots
= ±4x4
Answer: The square roots of 16x8 are ±4x4.
Find Roots
Answer: The opposite of the principal square root of (q3 + 5)4 is –(q3 + 5)2.
Find Roots
Answer:
Find Roots
Answer:
A. ±3x6
B. ±3x4
C. 3x4
D. ±3x2
A. Simplify .
A. –(a3 + 2)4
B. –(a3 + 2)8
C. (a3 + 2)4
D. (a + 2)4
B. Simplify .
A. 2xy2
B. ±2xy2
C. 2y5
D. 2xy
C. Simplify .
A. –4
B. ±4
C. –2
D. ±4i
D. Simplify .
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:
Simplify Using Absolute Value
Since the index is odd, you do not need absolute value.
Answer:
A. x
B. –x
C. |x|
D. 1
A. Simplify .
A. |3(x + 2)3|
B. 3(x + 2)3
C. |3(x + 2)6|
D. 3(x + 2)6
B. Simplify .
Approximate Radicals
Understand You are given the value for k.
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.
Plan Substitute the value for k into the formula. Use a calculator to evaluate.
Approximate Radicals
k = 3.5
Answer: The hole created by a particle traveling with energy of 3.5 joules will have a diameter of approximately 1.237 millimeters.
Use a calculator.
Solve Original formula
Approximate Radicals
Add 0.169 to each side.
Divide both sides by 0.926.
Cube both sides.
Simplify.
Check Original equation
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.
Approximate Radicals
d = 2.5
Answer: The hole with a diameter of 2.5 millimeters was created by a particle traveling with energy of 23.9 joules.
Use a calculator.
Solve Original formula
A. about 0.25 second
B. about 1.57 seconds
C. about 12.57 seconds
D. about 25.13 seconds
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 2.5 feet
B. about 10 feet
C. about 20.3 feet
D. about 25.5 feet
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?