Domanda del libro di testo
Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 21
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers.
Guida verificata passo dopo passo1
Identify the two expressions being multiplied: \(\sqrt{2x^2}\) and \(\sqrt{6x}\).
Recall the product rule for square roots: \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\), which allows us to combine the square roots into one.
Apply the product rule: \(\sqrt{2x^2} \cdot \sqrt{6x} = \sqrt{(2x^2)(6x)}\).
Multiply the expressions inside the square root: \((2x^2)(6x) = 12x^3\), so the expression becomes \(\sqrt{12x^3}\).
Simplify \(\sqrt{12x^3}\) by factoring inside the root to extract perfect squares, such as \(12 = 4 \times 3\) and \(x^3 = x^2 \times x\), then rewrite as \(\sqrt{4 \times 3 \times x^2 \times x}\).
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Product Rule for Radicals
The product rule for radicals states that the square root of a product equals the product of the square roots, i.e., √a * √b = √(a*b). This allows simplification by combining the radicands under a single square root before further simplification.
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Expanding Radicals
Properties of Exponents
When multiplying expressions with the same base, add their exponents: x^m * x^n = x^(m+n). This property helps simplify terms like x^2 * x by combining the powers into a single exponent.
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04:06Rational Exponents
Simplification of Radicals with Variables
When simplifying radicals involving variables, consider the domain (nonnegative real numbers) to safely apply square root properties. For example, √(x^2) = x if x ≥ 0, ensuring the expression remains valid and simplified.
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06:44Radical Expressions with Variables
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