Textbook Question
Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
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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 10
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+√25
Verified step by step guidance1
Identify the expression to evaluate: \(\sqrt{144} + \sqrt{25}\).
Recall that the square root function \(\sqrt{x}\) gives the non-negative number which, when squared, equals \(x\).
Calculate \(\sqrt{144}\) by finding the number that squared equals 144.
Calculate \(\sqrt{25}\) by finding the number that squared equals 25.
Add the two results together to get the value of the expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Roots
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √144 equals 12 because 12 × 12 = 144. Understanding how to find square roots is essential for evaluating expressions involving radicals.
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Imaginary Roots with the Square Root Property
Simplifying Radical Expressions
Simplifying radicals involves finding the principal square root and expressing the result in simplest form. When adding or subtracting square roots, only like radicals can be combined directly. In this problem, each root is simplified separately before performing addition.
Recommended video:
Guided course
05:45Radical Expressions with Fractions
Real Numbers and Roots
A real number root exists only if the radicand (the number under the root) is non-negative for even roots. If the radicand is negative, the root is not a real number. This concept helps determine whether the expression yields a real value or not.
Recommended video:
03:31Introduction to Complex Numbers
Related Practice
Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 4+5(x-7)3, for x =9
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Textbook Question
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x3+5x2−8x+9)+(17x3+2x2−4x−13)
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Textbook Question
Rewrite each expression without the absolute value bars. |√2-1|
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Textbook Question
In Exercises 1–10, factor out the greatest common factor. x2(2x+5)+17(2x+5)
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Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16
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