In Exercises 75-82, rationalize each denominator. Simplify, if possible (√(2))/(√(7))+(√(7))/(√(

step 1 In this question we have to rationalize under root 2 divide by root 7 plus root 7 divide by root

In Exercises 75-82, rationalize each denominator. Simplify,...

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Key Concepts

Radical Expressions

Radical expressions involve numbers or variables under a root symbol, such as a square root. These expressions obey specific arithmetic rules, including the properties of multiplication and division under radicals, which allow for operations like combining like terms or rewriting products of square roots as a single square root. Understanding these properties is essential when simplifying complex expressions involving radicals.

Rationalizing the Denominator

Rationalizing the denominator is a technique used to rewrite expressions so that no radicals appear in the denominator. This is accomplished by multiplying the numerator and denominator by an appropriate form of 1, such as the radical present in the denominator or its conjugate, to eliminate the square root or other radical from the denominator. This process yields an equivalent expression in a standardized form.

Simplification of Algebraic Expressions

Simplification of algebraic expressions involves restructuring and reducing expressions to their most concise form. In the context of expressions involving radicals, this includes applying rules of radical arithmetic, combining like terms, and ensuring that all radicals in denominators have been rationalized. The goal is to achieve an expression that is easier to interpret and use in further calculations.

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