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Properties of Radicals

• Simplify radical expressions using the product
rule for radicals

• Simplify radical expressions using the quotient
rule for radicals

Simplified Form of a Radical

A radical expression is in simplified form if all of the
following conditions are met:

1. The radicand has no factor raised to a
power greater than or equal to the index

2. There are no radicals in the denominator of
the fraction

3. The radicand does not contain a fraction.

Simplifying Radical Expressions
Condition1

Simplify
 

Simplify

Simplify

Product Rule for Radicals



Simplify

Simplify

Quotient Rule for Radicals



Simplifying Radical Expressions
Condition 2

Simplify

Simplify

Simplify

Simplify