Simplifying Radical Expressions Basic multiplication Basic division o Rationalize the denominator

Product Property of Radicals For any numbers a and b where and,

Examples:

Quotient Property of Radicals For any numbers a and b where and,

Examples:

What if the denominator still has a radical???????

Rationalizing the denominator Rationalizing the denominator means to remove any radicals from the denominator.

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Simplifying Radical Expressions Add Multiply o Conjugates

Adding radicals We can only combine terms with radicals if we have like radicals

Multiplying radicals - Distributive Property

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How do we rationalize a denominator like this???????

Conjugates The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

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