Radicals Simplify radical expressions using the properties of radicals

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Presentation transcript:

Radicals Simplify radical expressions using the properties of radicals Multiplying and dividing radical expressions using the properties of radicals Adding and subtracting radical expressions using the properties of radicals

Radical Notation n is called the index number a is called the radicand

Properties of Radicals

Simplifying Radicals The radicand has no factor raised to a power greater than or equal to the index number The radicand has no fractions No denominator contains a radical Exponents in the radicand and the index of the radical have no common factor All indicated operations have been performed

Simplify the following expressions

Simplifying Radicals If there is no index #, it is understood to be 2 When simplifying radicals use perfect squares, cubes, etc. Use factor trees to break a number into its prime factors Apply the properties of radicals and exponents

Simplify each of the following radicals Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers.

Simplify each of the following radicals Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers.

Rewrite each of the following as a single number under the radical sign

Multiplying Radicals Radicals must have the same index number Multiply outsides and insides together Add exponents when multiplying Simplify your expression Combine all like terms

Simplify each of the following radicals Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers.

Dividing Radicals No radicals in the denominator No fractions under the radical sign Apply the properties of radicals and exponents

Simplify each of the following radicals Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

Simplify each of the following radicals Simplify each of the following radicals. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

Add/Subtract Radicals Simplify each radical expression Radicals must have the same index number and same radicand Add the outside numbers together and the radicand remains the same

Simplify each of the following radicals

Mult/Dividing Radicals Simplify each of the following radicals

Mult/Dividing Radicals Multiply using fractional exponents and the properties of exponents. Write your answer in radical form and simplify. Multiply by changing the radicals to a common index and simplify.