Textbook Question
Determine whether each statement is true or false. {x | x is a natural number less than 3}= {1, 2}
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Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 1, Problem 49
Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √11 • √44
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Recall the product rule for radicals: \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\), where \(a\) and \(b\) are positive real numbers.
Apply the product rule to the given expression: \(\sqrt{11} \cdot \sqrt{44} = \sqrt{11 \times 44}\).
Multiply the numbers inside the radical: \(11 \times 44\).
Express the product inside the radical as a single number: \(\sqrt{484}\).
Simplify the square root if possible by finding the square root of \(484\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Radicals
Radicals represent roots, commonly square roots, and follow specific properties such as √a * √b = √(a*b) when a and b are non-negative. Understanding these properties allows simplification of expressions involving roots by combining or separating them.
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05:20
Expanding Radicals
Multiplication of Radicals
When multiplying radicals with the same index, multiply the radicands (the numbers inside the roots) directly under a single radical. For example, √11 * √44 = √(11*44), which simplifies the expression and makes further simplification possible.
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05:20Expanding Radicals
Simplifying Radicals
After combining radicals, simplify the resulting radical by factoring out perfect squares from the radicand. For instance, √484 can be simplified to 22 because 484 is 22 squared. This step makes the expression easier to interpret and use.
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5:48Adding & Subtracting Unlike Radicals by Simplifying
Related Practice
Textbook Question
Find each product. See Examples 5 and 6.
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Textbook Question
Find each product. (5r-3t2)2
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Textbook Question
Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers. 48/46
Textbook Question
Multiply or divide, as indicated. ac + ad + bc + bd/a2 - b2 * a3 - b3/2a2 + 2ab + 2b2
Textbook Question
Factor each trinomial, if possible. See Examples 3 and 4.
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