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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.

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

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 #

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:

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

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

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:

7.2 – Rational Exponents More Examples: or

7.2 – Rational Exponents or or Examples: or

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

7.3 – Simplifying Rational Expressions
Product Rule for Square Roots Examples:

7.3 – Simplifying Rational Expressions
Quotient Rule for Square Roots Examples:

7.3 – Simplifying Rational Expressions

7.3 – Simplifying Rational Expressions
Examples:

7.3 – Simplifying Rational Expressions
Examples:

7.3 – Simplifying Rational Expressions
One Big Final Example

Review and Examples: