Domanda del libro di testo
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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TOC.tableOfContents
- 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
Capitolo 1, Problema 10
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+√25
Guida verificata passo dopo passo1
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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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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02:20
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.
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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.
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03:31Introduction to Complex Numbers
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