Domanda del libro di testo
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17
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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 68
Simplify the radical expressions in Exercises 67–74, if possible. ³√150
Guida verificata passo dopo passo1
Identify the type of radical expression: This is a cube root (³√) of 150. The goal is to simplify it by factoring the radicand (the number inside the radical) into its prime factors.
Perform prime factorization of 150: Break 150 into its prime factors. Start by dividing by the smallest prime numbers. For example, 150 = 2 × 3 × 5².
Group the factors into sets of three (since it is a cube root): Look for any factor that appears three times, as it can be taken out of the cube root. In this case, there are no factors that appear three times.
Simplify the expression: Since no factor appears three times, the cube root cannot be simplified further. The expression remains as ³√150.
Conclude the solution: State that the simplified form of the cube root of 150 is ³√150, as no further simplification is possible.
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Radical Expressions
Radical expressions involve roots, such as square roots or cube roots. They can be simplified by factoring the radicand (the number inside the root) into its prime factors and identifying perfect powers. Understanding how to manipulate these expressions is crucial for simplification.
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05:45
Radical Expressions with Fractions
Cube Roots
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, ³√8 = 2 because 2 × 2 × 2 = 8. Recognizing perfect cubes within the radicand helps in simplifying cube root expressions effectively.
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02:20Imaginary Roots with the Square Root Property
Prime Factorization
Prime factorization is the process of breaking down a number into its prime factors. This technique is essential for simplifying radical expressions, as it allows one to identify and extract perfect squares or cubes from the radicand, facilitating the simplification process.
Video consigliato:
07:30Introduction to Factoring Polynomials
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