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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. radical sign index radicand This symbol is the radical or the radical sign The expression under the radical sign is the radicand. The index defines the root to be taken.

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**Introduction to Radicals**

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

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**Introduction to Radicals**

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

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**Introduction to Radicals**

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

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**Introduction to Radicals**

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

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**Introduction to Radicals**

nth Roots An nth root of any number a is a number whose nth power is a. Examples:

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**Introduction to Radicals**

nth Roots An nth root of any number a is a number whose nth power is a. Examples: Non-real number Non-real number

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**Introduction to Radicals**

Radicals with Variables Examples:

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**Simplifying Radicals using the Product Rule**

Product Rule for Square Roots Examples:

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**Simplifying Radicals using the Quotient Rule**

Quotient Rule for Square Roots Examples:

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**Simplifying Radicals Containing Variables**

Examples:

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**Simplifying Cube Roots**

Simplifying Radicals Simplifying Cube Roots Examples:

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Simplifying Radicals Examples:

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Simplifying Radicals Examples:

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Day One Stop Here

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**Adding and Subtracting Radicals**

Review and Examples:

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**Adding and Subtracting Radicals**

Simplifying Radicals Prior to Adding or Subtracting

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**Adding and Subtracting Radicals**

Simplifying Radicals Prior to Adding or Subtracting

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