Question

Rationalize the denominator. $$5 a 2 b 5 a b 2-\sqrt{3}$$

   Rationalize the denominator.
$$5 a 2 b 5 a b 2-\sqrt{3}$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 8, Problem 62

Instant Answer

Solved by Expert Victor Salazar

02/03/2022

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The question asks to rationalize the denominator of a given expression, but the explanation seems to be solving a quadratic equation. Therefore, it's not possible to provide a step-by-step solution based on the given explanation. However, if we were to Show more…

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Rationalize the denominator. $$5 a 2 b 5 a b 2-\sqrt{3}$$

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Key Concepts

Simplification of Algebraic Expressions

Simplification of algebraic expressions involves rewriting expressions in an equivalent, often more manageable form. This can include combining like terms, reducing fractions, and eliminating radicals from denominators, all of which are important techniques in algebra.

Difference of Squares

The difference of squares is an algebraic identity that expresses the product of a sum and a difference (e.g., (a + b)(a - b)) as the difference of their squares (a² - b²). This identity is essential when using the conjugate method to eliminate radicals from the denominator.

Conjugate Method

The conjugate method is used when faced with a binomial denominator containing a radical. By multiplying both the numerator and the denominator by the conjugate of the denominator, the expression utilizes the difference of squares to remove the radical, thereby rationalizing the denominator.

Rationalization

Rationalization is the process of eliminating irrational numbers, such as square roots, from the denominator of a fraction. This step is taken to simplify the expression and make it easier to work with in further calculations, ensuring that the denominator is a rational number.

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