Domanda del libro di testo
Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)
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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 45
Rationalize the denominator.
Guida verificata passo dopo passo1
Identify the expression to rationalize: \(\frac{1}{\sqrt7}\), where the denominator contains a square root.
To rationalize the denominator, multiply both the numerator and the denominator by \(\sqrt7\) to eliminate the square root in the denominator.
Write the multiplication as: \(\frac{1}{\sqrt7} \times \frac{\sqrt7}{\sqrt7}\).
Multiply the numerators together and the denominators together: numerator becomes \(1 \times \sqrt7 = \sqrt7\), denominator becomes \(\sqrt7 \times \sqrt7 = 7\).
Rewrite the expression with the rationalized denominator as \(\frac{\sqrt7}{7}\).
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Rationalizing the Denominator
Rationalizing the denominator involves eliminating any irrational numbers, such as square roots, from the denominator of a fraction. This is done by multiplying the numerator and denominator by a suitable expression that removes the radical, making the expression easier to interpret and use in further calculations.
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02:58
Rationalizing Denominators
Properties of Square Roots
Square roots represent a number which, when multiplied by itself, gives the original number. Understanding that √a × √a = a is essential for rationalizing denominators, as multiplying by the square root in the denominator can simplify the expression by removing the radical.
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02:20Imaginary Roots with the Square Root Property
Multiplying Fractions by 1
Multiplying a fraction by a form of 1, such as √7/√7, does not change its value but can change its form. This technique is used to rationalize denominators by creating an equivalent fraction with a rational denominator, facilitating easier manipulation and simplification.
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04:15Multiply Polynomials Using the Distributive Property
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