Textbook Question
In Exercises 47 - 49, add or subtract terms whenever possible. 4√72 - 2√48
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 50
Rationalize the denominator. 30/√5
Verified step by step guidance1
Identify the expression to rationalize: \(\frac{30}{\sqrt{5}}\).
Recall that rationalizing the denominator means eliminating the square root from the denominator by multiplying numerator and denominator by the same radical.
Multiply both numerator and denominator by \(\sqrt{5}\) to get \(\frac{30}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}\).
Use the property \(\sqrt{a} \times \sqrt{a} = a\) to simplify the denominator: \(\sqrt{5} \times \sqrt{5} = 5\).
Write the new expression as \(\frac{30 \times \sqrt{5}}{5}\) and simplify the fraction if possible.
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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 both the numerator and denominator by a suitable expression that will remove the radical from the denominator.
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Rationalizing Denominators
Properties of Square Roots
Square roots have properties that allow simplification, such as √a × √a = a. Understanding these properties helps in manipulating expressions to rationalize denominators by converting radicals into whole numbers.
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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 √5/√5, changes the expression without altering its value. This technique is essential for rationalizing denominators because it allows the removal of radicals while keeping the fraction equivalent.
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Related Practice
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In Exercises 33–68, add or subtract as indicated.
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