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# 15.1 – Introduction to Radicals PowerPoint PPT Presentation

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.

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#### Presentation Transcript

Finding a root of a number is the inverse operation of raising a number to a power.

index

The index defines the root to be taken.

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 #

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

What does the following symbol represent?

The symbol represents the negative root of a number.

What is the index of the expression ?

3

Cube Roots

A cube root of any positive number is positive.

A cube root of any negative number is negative.

Examples:

nth Roots

An nth root of any number a is a number whose nth power is a.

Examples:

nth Roots

An nth root of any number a is a number whose nth power is a.

Examples:

Non-real number

Non-real number

Examples:

Simplifying Radicals using the Product Rule

Product Rule for Square Roots

Examples:

Simplifying Radicals using the Quotient Rule

Quotient Rule for Square Roots

Examples:

Examples:

Simplifying Cube Roots

Examples:

Examples:

Examples: