Domanda del libro di testo
In Exercises 49–56, factor each perfect square trinomial. x^2−14x+49
194
views
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 51
Rationalize the denominator.
Guida verificata passo dopo passo1
Identify the expression to rationalize: \(\frac{7}{\sqrt{5} - 2}\), where the denominator contains a radical.
To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \(\sqrt{5} - 2\) is \(\sqrt{5} + 2\).
Set up the multiplication: \(\frac{7}{\sqrt{5} - 2} \times \frac{\sqrt{5} + 2}{\sqrt{5} + 2}\).
Multiply the numerators: \(7 \times (\sqrt{5} + 2)\), and multiply the denominators using the difference of squares formula: \((\sqrt{5})^2 - (2)^2\).
Simplify the denominator to \(5 - 4\), and write the expression as \(\frac{7(\sqrt{5} + 2)}{1}\), which completes the rationalization process.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Rationalizing the Denominator
Rationalizing the denominator involves eliminating any irrational numbers, such as square roots, from the denominator of a fraction. This is done to simplify the expression and make it easier to work with or interpret.
Video consigliato:
02:58
Rationalizing Denominators
Conjugates of Binomials
The conjugate of a binomial expression a + b is a - b, and vice versa. Multiplying a binomial by its conjugate results in a difference of squares, which helps eliminate square roots in the denominator.
Video consigliato:
05:33Complex Conjugates
Difference of Squares Formula
The difference of squares formula states that (a + b)(a - b) = a² - b². This property is used when multiplying by the conjugate to remove radicals from the denominator by turning it into a rational number.
Video consigliato:
04:14Special Products - Square Formulas
Pratica correlata
Domanda del libro di testo
Rationalize the denominator.
636
views
Domanda del libro di testo
Rationalize the denominator. √2/√3
244
views
Domanda del libro di testo
In Exercises 15–58, find each product. (x+2)3
1032
views
Domanda del libro di testo
Simplify each exponential expression in Exercises 23–64.
292
views
Domanda del libro di testo
Rewrite each expression without absolute value bars. |300|
1271
views