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?