R8 Radicals and Rational Exponents

Radical Notation

n is called the index number

a is called the radicand

Properties of Radicals

Simplifying Radicals

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

2.The radicand has no fractions.

3.No denominator contains a radical.

4.Exponents in the radicand and the index of the radical have no common factor.

5.All indicated operations have been performed

• 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

Simplifying Radicals

Simplifying Radicals

Simplify each radical expression

Assume that all variables represent nonnegative real

numbers.

Assume that all variables represent nonnegative real

numbers.

Rewrite each of the following as a single number under the

radical sign.

Multiplying Radicals

1.Radicals must have the same index number

2.Multiply outsides and insides together

3.Add exponents when multiplying

4.Simplify your expression

5.Combine all like terms

Assume that all variables represent nonnegative real

numbers.

Assume that all variables represent nonnegative real

numbers.

Add/Subtract Radicals

1.Simplify each radical expression

2.Radicals must have the same index number and same radicand

3.Add the outside numbers together and the radicand remains the same

Simplify each of the following radicals.

Simplify each of the following radicals.

Dividing Radicals1.No radicals in the

denominator

2.No fractions under the radicand

3.Apply the properties of radicals and exponents

Assume that all variables represent nonnegative real

numbers and that no denominators are zero.

Assume that all variables represent nonnegative real

numbers and that no denominators are zero.

Assume that all variables represent nonnegative real

numbers and that no denominators are zero.

Assume that all variables represent nonnegative real

numbers and that no denominators are zero.

Simplify each of the following radicals.

Rational Exponents

Rational Exponents

Simplify each expression containing fractional exponents

as radicals.

Simplify each expression using radicals and exponents.

Simplify each expression using radicals or exponents.

Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the

variables are positive.

Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the

variables are positive.

Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the

variables are positive.