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Concept
(1)

We have **rational functions** whenever we have a fraction that has a polynomial in the numerator and/or in the denominator. An excluded value in the function is any value of the variable that would make the denominator equal to zero. To find the domain, list all the values of the variable that, when substituted, would result in a zero in the denominator.

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Sample Problems
(10)

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Problem 1

How to simplify radicands that are whole numbers.

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Problem 2

Two methods for simplifying radical expressions that do not have variables.

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Problem 3

Simplifying radicals in the context of using the Pythagorean Theorem to find a missing side length of a right triangle.

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Problem 4

Simplifying radical expressions with integers and variables by re-writing with perfect square factors.

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Problem 5

Simplifying division of radical expressions where both terms are roots of perfect squares.

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Problem 6

Introduction to radicals, including notation, square root, cube roots, principal roots, and square roots of perfect squares.

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Problem 7

Simplifying radicals in the Pythagorean Theorem.

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Problem 8

Exact, simple radical form answers versus decimal approximations from rounding on a calculator.

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Problem 9

Re-writing radical monomials as terms with fractional exponents.

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Problem 10

Simplifying fractions with a radical binomial in the numerator, maintaining simple radical form.