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.

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

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

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

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

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

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

Radicals with Variables Examples: Introduction to Radicals

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

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

Simplifying Radicals Containing Variables Examples: Simplifying Radicals

Simplifying Cube Roots Examples: Simplifying Radicals

Examples: Simplifying Radicals

Examples: Simplifying Radicals

Day One Stop Here

Review and Examples: Adding and Subtracting Radicals

Simplifying Radicals Prior to Adding or Subtracting Adding and Subtracting Radicals

Simplifying Radicals Prior to Adding or Subtracting Adding and Subtracting Radicals