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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. R - Algebra ReviewProblem 65
Chapter 1, Problem 65

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √5 /√20

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Identify the expression to simplify: \(\frac{\sqrt{5}}{\sqrt{20}}\).
Use the quotient rule for radicals, which states that \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\), to rewrite the expression as \(\sqrt{\frac{5}{20}}\).
Simplify the fraction inside the radical: \(\frac{5}{20} = \frac{1}{4}\).
Rewrite the expression as \(\sqrt{\frac{1}{4}}\).
Use the product rule for radicals to separate the square root of the fraction: \(\sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}}\), then simplify each radical.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Product Rule for Radicals

The product rule for radicals states that the square root of a product equals the product of the square roots: √(a * b) = √a * √b. This rule allows simplification by breaking down complex radicals into simpler factors, making it easier to simplify or combine expressions.
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Quotient Rule for Radicals

The quotient rule for radicals states that the square root of a quotient equals the quotient of the square roots: √(a / b) = √a / √b, where b ≠ 0. This rule helps in rewriting expressions involving division under a radical sign into a simpler form.
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Simplifying Radicals

Simplifying radicals involves expressing the radicand as a product of perfect squares and other factors, then applying the product rule to extract square roots of perfect squares. For example, √20 can be simplified to 2√5 by factoring 20 as 4 * 5.
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