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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. R - Algebra ReviewProblema 93
Capitolo 1, Problema 93

Add or subtract, as indicated. See Example 6. 5√3 + √12

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1
Identify the terms to be added: \(5\sqrt{3}\) and \(\sqrt{12}\).
Simplify the square root in the second term: \(\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}\).
Rewrite the expression with the simplified term: \(5\sqrt{3} + 2\sqrt{3}\).
Since both terms have the same radical part (\(\sqrt{3}\)), combine the coefficients: \((5 + 2)\sqrt{3}\).
Express the final simplified form as \(7\sqrt{3}\) (do not calculate the decimal value).

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Simplifying Radicals

Simplifying radicals involves expressing a square root in its simplest form by factoring out perfect squares. For example, √12 can be simplified to 2√3 because 12 = 4 × 3 and √4 = 2. This step is essential before performing addition or subtraction of radicals.
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Simplifying Trig Expressions

Like Radicals

Like radicals have the same radicand (the number inside the square root). Only like radicals can be added or subtracted directly by combining their coefficients. For instance, 5√3 and 2√3 are like radicals and can be combined as (5 + 2)√3 = 7√3.
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Rationalizing Denominators

Adding and Subtracting Radicals

To add or subtract radicals, first simplify them and ensure they are like radicals. Then, add or subtract their coefficients while keeping the radical part unchanged. This process is similar to combining like terms in algebra.
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Adding and Subtracting Complex Numbers
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Factor each polynomial completely. See Example 6. t⁴ - 1

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Simplify each inequality if needed. Then determine whether the statement is true or false. -6 < 7 + 3

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Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]

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(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.

Distance = (7 − x) / (0.639x + 1.75)

For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the distance from the origin is

Distance ≈ (7 − 0.6) / (0.639 × 0.6 + 1.75) ≈ 3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) What is the distance from the origin of the Nile when the river has an altitude of 7000 ft?

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Add or subtract, as indicated. See Example 6. √45 + 4√20

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Simplify each inequality if needed. Then determine whether the statement is true or false. 2 • 5 ≥ 4 + 6

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