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15.1 – Introduction to Radicals

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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:

15.2 – 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

15.3 – Adding and Subtracting Radicals

Simplifying Radicals Prior to Adding or Subtracting