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Factor out the greatest common factor.
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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 1
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √36
Guida verificata passo dopo passo1
Recognize that the problem involves finding the square root of 36, which is written as √36.
Recall the definition of a square root: The square root of a number is a value that, when multiplied by itself, equals the original number.
Determine if the number under the square root (36) is a perfect square. A perfect square is a number that can be expressed as the square of an integer.
Since 36 is a perfect square (6 × 6 = 36), the square root of 36 is a real number.
Conclude that the square root of 36 is the positive value of the integer that satisfies the equation x² = 36.
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Square Roots
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 36 is 6, since 6 × 6 = 36. Square roots can be both positive and negative, but in most contexts, the principal (non-negative) square root is used.
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02:20
Imaginary Roots with the Square Root Property
Real Numbers
Real numbers include all the numbers on the number line, encompassing rational numbers (like integers and fractions) and irrational numbers (like √2 or π). When evaluating square roots, it's important to determine if the result is a real number; for instance, the square root of a negative number is not a real number.
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03:31Introduction to Complex Numbers
Evaluating Expressions
Evaluating an expression involves substituting values into the expression and simplifying it to find a numerical result. In the case of square roots, this means determining the value that satisfies the equation x² = the given number, ensuring that the result is a real number when applicable.
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03:11Evaluating Algebraic Expressions
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