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**7.1 – Radicals Radical Expressions**

Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical or the radical sign radical sign index radicand The expression under the radical sign is the radicand. The index defines the root to be taken.

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**7.1 – Radicals Radical Expressions**

The above symbol represents the positive or principal root of a number. The symbol represents the negative root of a number.

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**7.1 – 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 #

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**7.1 – Radicals Rdicals Cube Roots**

A cube root of any positive number is positive. A cube root of any negative number is negative. Examples:

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

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7.1 – 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

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7.2 – Rational Exponents The value of the numerator represents the power of the radicand. The value of the denominator represents the index or root of the expression. Examples:

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7.2 – Rational Exponents More Examples: or

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7.2 – Rational Exponents or or Examples: or

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7.2 – Rational Exponents Use the properties of exponents to simplify each expression

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**7.3 – Simplifying Rational Expressions**

Product Rule for Square Roots Examples:

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**7.3 – Simplifying Rational Expressions**

Quotient Rule for Square Roots Examples:

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**7.3 – Simplifying Rational Expressions**

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**7.3 – Simplifying Rational Expressions**

Examples:

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**7.3 – Simplifying Rational Expressions**

Examples:

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**7.3 – Simplifying Rational Expressions**

One Big Final Example

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**7.4 – Adding, Subtracting, Multiplying Radical Expressions**

Review and Examples:

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**7.4 – Adding, Subtracting, Multiplying Radical Expressions**

Simplifying Radicals Prior to Adding or Subtracting

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**7.4 – Adding, Subtracting, Multiplying Radical Expressions**

Simplifying Radicals Prior to Adding or Subtracting

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**7.4 – Adding, Subtracting, Multiplying Radical Expressions**

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**7.4 – Adding, Subtracting, Multiplying Radical Expressions**

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**7.4 – Adding, Subtracting, Multiplying Radical Expressions**

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