Textbook Question
Rationalize the denominator.
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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
Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)
Verified step by step guidance1
Identify the expression given: \(\sqrt{\frac{121}{4}}\). This is a square root of a fraction.
Recall the property of square roots that allows you to separate the root of a fraction into the root of the numerator over the root of the denominator: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\).
Apply this property to the expression: \(\sqrt{\frac{121}{4}} = \frac{\sqrt{121}}{\sqrt{4}}\).
Simplify the square roots of the numerator and denominator separately: \(\sqrt{121}\) and \(\sqrt{4}\).
Write the simplified expression as a fraction of the simplified roots: \(\frac{\sqrt{121}}{\sqrt{4}}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quotient Rule for Radicals
The quotient rule for radicals states that the square root of a quotient is equal to the quotient of the square roots, i.e., √(a/b) = √a / √b, provided b ≠ 0. This rule allows simplification of expressions involving roots of fractions by separating numerator and denominator.
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Product, Quotient, and Power Rules of Logs
Simplifying Square Roots
Simplifying square roots involves finding the prime factors or perfect squares within the radicand to rewrite the root in simplest form. For example, √121 = 11 because 121 is a perfect square, which helps in reducing expressions to their simplest terms.
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02:20Imaginary Roots with the Square Root Property
Properties of Fractions
Understanding fractions is essential when working with radicals in quotient form. Recognizing that a fraction like 121/4 can be expressed as (121)/(4) helps apply the quotient rule correctly and simplifies the expression by dealing with numerator and denominator separately.
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5:36Change of Base Property
Related Practice
Textbook Question
In Exercises 15–58, find each product. (x−3)2
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Textbook Question
In Exercises 45–54, rationalize the denominator. 2/√10
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Simplify each exponential expression in Exercises 23–64.
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In Exercises 33–68, add or subtract as indicated. 3x/8 + x/12
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Textbook Question
In Exercises 39–48, factor the difference of two squares. 36x2−49y2
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