15.1 – Introduction to Radicals

15.1 – 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.

15.1 – 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 #

15.1 – 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

15.1 – 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

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

15.1 – Introduction to Radicals nth Roots An nth root of any number a is a number whose nth power is a. Examples:

15.1 – 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

15.1 – Introduction to Radicals Radicals with Variables Examples:

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

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

15.2 – Simplifying Radicals Simplifying Radicals Containing Variables Examples:

15.2 – Simplifying Radicals Simplifying Cube Roots Examples:

15.2 – Simplifying Radicals Examples:

15.3 – Adding and Subtracting Radicals Review and Examples:

15.3 – Adding and Subtracting Radicals Simplifying Radicals Prior to Adding or Subtracting

15.1 – Introduction to Radicals