Textbook Question
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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Table of contents
- 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
Chapter 1, Problem 45
Rationalize the denominator.
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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
Related Practice
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