Textbook Question
Solve each inequality. Give the solution set in interval notation. 1≤(4x-5)/2<9
Ch. 1 - Equations and Inequalities
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 2, Problem 37a
Find each product or quotient. Simplify the answers. √-10 / √-40
Verified step by step guidance1
Recognize that the problem involves the quotient of two square roots with negative radicands: \(\frac{\sqrt{-10}}{\sqrt{-40}}\).
Rewrite each square root of a negative number using the imaginary unit \(i\), where \(i = \sqrt{-1}\). So, \(\sqrt{-10} = \sqrt{10} \cdot i\) and \(\sqrt{-40} = \sqrt{40} \cdot i\).
Substitute these into the expression: \(\frac{\sqrt{10} \cdot i}{\sqrt{40} \cdot i}\).
Cancel the common factor \(i\) in numerator and denominator, leaving \(\frac{\sqrt{10}}{\sqrt{40}}\).
Simplify the quotient of square roots by writing it as \(\sqrt{\frac{10}{40}}\) and then simplify the fraction inside the square root before simplifying the radical.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simplifying Square Roots of Negative Numbers
Square roots of negative numbers involve imaginary numbers, since the square root of a negative value is not real. This is expressed using the imaginary unit 'i', where i² = -1. For example, √-10 can be rewritten as √10 × i.
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Square Roots of Negative Numbers
Properties of Radicals in Division
When dividing square roots, the quotient rule applies: √a / √b = √(a/b), provided a and b are non-negative. This property helps simplify expressions by combining radicals under a single root before further simplification.
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Simplifying Radicals by Factoring
Simplifying radicals often involves factoring the number inside the root into perfect squares and other factors. Extracting the square root of perfect squares simplifies the expression, such as √40 = √(4×10) = 2√10.
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5:48Adding & Subtracting Unlike Radicals by Simplifying
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