Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. R - Algebra Review

Problema 91

Capitolo 1, Problema 91

Add or subtract, as indicated. See Example 6. √6 + √7

Guida verificata passo dopo passo

Identify the terms involved: \( \sqrt{6} \) and \( \sqrt{7} \). Both are square roots of different numbers.

Recall that square roots can only be combined through addition or subtraction if they have the same radicand (the number inside the root). Here, \( \sqrt{6} \) and \( \sqrt{7} \) have different radicands.

Since the radicands are different, these terms are unlike radicals and cannot be simplified by addition or subtraction directly.

Therefore, the expression \( \sqrt{6} + \sqrt{7} \) remains as it is because it cannot be combined further.

If needed, you can approximate each square root separately using a calculator, but the exact simplified form is just the sum of the two square roots.

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Simplifying Radicals

Simplifying radicals involves expressing square roots in their simplest form by factoring out perfect squares. This helps in identifying like terms and making addition or subtraction possible. For example, √18 can be simplified to 3√2 by factoring 18 as 9×2.

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Percorso guidato

6:36

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, 2√3 + 5√3 equals 7√3, but √6 + √7 cannot be combined since 6 and 7 differ.

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Percorso guidato

2:58

Rationalizing Denominators

Addition and Subtraction of Radicals

Adding or subtracting radicals requires first simplifying them and then combining only like radicals. If radicals are unlike, they remain separate terms in the expression. This concept is similar to combining like terms in algebra, ensuring operations are valid.

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Percorso guidato

3:18

Adding and Subtracting Complex Numbers

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Factor each polynomial completely. See Example 6. 8t³ + 125

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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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Simplify each inequality if needed. Then determine whether the statement is true or false. 7 ≤ 7

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Simplify each inequality if needed. Then determine whether the statement is true or false. 0 ≤ -5

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