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 Depdendent Variable

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 Dependent Variable

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Square Roots

 Square Root  The number c is a square root of a if c2=a

Ex. Find the roots of…

 Principal Square Root   The principal square root of a nonnegative number is its nonnegative square root.The symbol is called a radical sign and is used to indicate the principal square root of the number over which it appears

Ex. Find the principal root of…

Properties of Square Roots
o Every positive real number has _________ real-numbered square roots
o The square root of zero is _________
o The square root of a negative number is _________ *
o The principal square root of a non-negative number is its _________

Graphs of radical functions and their domains

Ex. Graph f (x) =and find the domain

Ex. Graph g(x) =and find the domain

What is the principal square root of a2
Ex. Find

 Simplifying For any real number a , (The principal square root of a2 is the absolute value of a.)

Ex. Find the principal square roots

Cube Roots

 Cube Root The number c is the cube root of a if c3 =a.In symbols,we write to denote the cube root of a.

Ex. Find the cube roots of…

Ex. Graph f (x) =and find the domain

Ex. Simplifying the Cube Roots

What are the nth roots?

• The fourth root of a number a is the number c for which c4 = a .There are
also 5th roots, 6th roots, and so on.
• We writefor the nth root.
• The number n is called the index (plural, indices). When the index is 2, we
do not write it.

Summary of Roots

Section 10.2 Rational Exponents

What are rational exponents?

 means when a is nonnegative,n can be any natural number greater 1.when a is negative ,n must be odd.

 Positive Rational Exponents For any natural numbers m and n(n≠1) and any real number a for which exists   and ,or

 Negative Rational Exponents For any rational number m/n and any nonzero real number a for which am/n exists   means

Ex. Approximate the following on your calculator. Round to 4 decimal places

Ex. Re-write each expression as a radical and evaluate

 Laws of exponents For any real numbers a and b and any rational exponents m and n for which am,an and bm are defined 1.am•an = am+n 2.am/an =am-n 3.(am)n=amn4.(ab)m=ambm In multiplying,add exponents if the bases are the same In deviding,extract exponents if the bases are the same.(Assume a≠0.) To raise a power to a power ,multiply the exponents To raise a product to a power,raise each factor to the power and multiply.

Ex. Simplify…

Ex. Use rational exponents to simplify … write as a radical, when appropriate

 The Product Rule for Radicals For any real numbers and (The product of nth roots is the nth root of the product of the two radicands)

Ex. Multiply

Ex. Divide

Simplifying by factoring

 To simplify a Radical expression with Index n by Factoring. 1.Express the radicand  as a product in which one factor is the largest perfect nth power possible . 2.Take the nth root of each factor. 3.Simplication is complete when no radicand has a factor that is a perfect nth power.

Ex. Simplify

Ex. Simplify

Ex. Multiply and Simplify

Section 10.4 Dividing Radicals and Rationalizing Denominators

 The Quotient Rule for Radicand For any real numbers and and b≠0

Rationalizing Denominators

Section 10.5 Expressions Containing Several Radical Terms

More Multiplication and Division
• Use the Distributive Property, FOIL, etc…