nth root radical sign index radicand principal root

Find Roots = ± 4 x 4 Answer: The square roots of 16 x

Find Roots Answer: The opposite of the principal square root of (q 3 +

Simplify Using Absolute Value Note that t is a sixth root of t 6.

Simplify Using Absolute Value Since the index is odd, you do not need absolute

Approximate Radicals A. SPACE Designers must create satellites that can resist damage from being

Approximate Radicals Solve Original formula k = 3. 5 Use a calculator. Answer: The

Approximate Radicals Check Original equation Add 0. 169 to each side. Divide both sides

Approximate Radicals B. SPACE Designers must create satellites that can resist damage from being

Approximate Radicals Solve Original formula d = 2. 5 Use a calculator. Answer: The

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• nth root • radical sign • index • radicand • principal root

Find Roots = ± 4 x 4 Answer: The square roots of 16 x 8 are ± 4 x 4.

Find Roots Answer: The opposite of the principal square root of (q 3 + 5)4 is –(q 3 + 5)2.

Find Roots Answer:

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:

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.

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.

Approximate Radicals Check Original equation Add 0. 169 to each side. Divide both sides by 0. 926. Cube both sides. Simplify.

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 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.