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Introduction to Radicals Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical or the radical sign index radical sign radicand The expression under the radical sign is the radicand. The index defines the root to be taken.

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Square Roots If a is a positive number, then is the positive square root of a and is the negative square root of a. A square root of any positive number has two roots – one is positive and the other is negative. Examples: non-real # Introduction to Radicals

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What does the following symbol represent? The symbol represents the positive or principal root of a number. Introduction to Radicals What is the radicand of the expression ? 5xy

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What does the following symbol represent? The symbol represents the negative root of a number. Introduction to Radicals What is the index of the expression ? 3

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Cube Roots A cube root of any positive number is positive. Examples: A cube root of any negative number is negative. Introduction to Radicals

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n th Roots An n th root of any number a is a number whose n th power is a. Examples: Introduction to Radicals

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n th Roots An n th root of any number a is a number whose n th power is a. Examples: Non-real number Introduction to Radicals

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Radicals with Variables Examples: Introduction to Radicals

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Simplifying Radicals Simplifying Radicals using the Product Rule Examples: Product Rule for Square Roots

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Simplifying Radicals using the Quotient Rule Examples: Quotient Rule for Square Roots Simplifying Radicals

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Simplifying Radicals Containing Variables Examples: Simplifying Radicals

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Simplifying Cube Roots Examples: Simplifying Radicals

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Examples: Simplifying Radicals

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Examples: Simplifying Radicals

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Day One Stop Here

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Review and Examples: Adding and Subtracting Radicals

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Simplifying Radicals Prior to Adding or Subtracting Adding and Subtracting Radicals

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Simplifying Radicals Prior to Adding or Subtracting Adding and Subtracting Radicals

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