RADICALS ARE SO RAD DUDE!!!! 7.1 nth Roots and Rational Exponents In this section, we will… Use rational exponent notation Find nth roots Evaluate and simplify radical expression RADICALS ARE SO RAD DUDE!!!!

Recall from Review … If a is a non-negative real number, any number b, such that is the square root of a and is denoted Examples: Evaluate the following by taking the square root. Negative numbers do not have real # square roots 7.1 nth Roots and Rational Expressions: nth Roots

RAD-TASTIC MATHEMATICS Vocabulary Important Properties  

Rewrite the expression using rational exponent notation.   RAD-RRIFIC EXAMPLES  

Rewrite the expression using radical notation.   Examples with SWAGGER!  

I’m too smart for my calculator!!! Evaluate the expression WITHOUT a calculator.   I’m too smart for my calculator!!!  

Friday 10/7/11 Homework Pg. 404 #13-22, #29-40 (even) THANK YOU FOR THE EXTRA PRACTICE MS. POBUDA!! Friday 10/7/11 Homework Pg. 404 #13-22, #29-40 (even)

Section 7.1 Radical refreshment

WHITEBOARDIN G

Real World Uses of Square Roots http://www.youtube.com/watch?v=_TrFzF0ZE00

Properties of rational exponents Section 7.2 Properties of rational exponents

Simplifying Expressions Containing Rational Exponents: Laws of Exponents: For any integers m, n (assuming no divisions by 0) and new! new! Recognize these?!?! 7.1 nth Roots and Rational Expressions: Simplify Expressions with Rational Exponents

Properties of Exponents Applied to Radicals: Simplifying Radicals: A radical is in simplest form when: No radicals appear in the denominator of a fraction The radicand cannot have any factors that are perfect roots (given the index) Examples: Simplify each expression. 7.1 nth Roots and Rational Expressions: nth Roots

Simplifying Radical Expressions Containing Variables: Examples: Simplify each expression. Assume that all variables are positive. When we divide the exponent by the index, the remainder remains under the radical 7.1 nth Roots and Rational Expressions: nth Roots

Multiplying and Dividing Radical Expressions: Examples: Simplify each expression. Assume that all variables are positive. 7.1 nth Roots and Rational Expressions: Add, Subtract, Multiply and Divide Radicals

Rationalizing Denominators: Recall that simplifying a radical expression means that no radicals appear in the denominator of a fraction. Examples: Simplify each expression. Assume that all variables are positive. 7.1 nth Roots and Rational Expressions: Rationalize Denominators

Adding and Subtracting Radical Expressions: simplify each radical expression combine all like-radicals (combine the coefficients and keep the common radical) Examples: Simplify each expression. Assume that all variables are positive. 7.1 nth Roots and Rational Expressions: nth Roots

Examples: Simplify each expression Examples: Simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. 7.1 nth Roots and Rational Expressions: Simplify Expressions with Rational Exponents

Examples: Simplify each expression Examples: Simplify each expression. Assume that all variables are positive. 7.1 nth Roots and Rational Expressions: Add, Subtract, Multiply and Divide Radicals

Radical Maze

where is the initial velocity in ft/sec of the object. Example: The final velocity, v, of an object in feet per second (ft/sec) after it slides down a frictionless inclined plane of height h feet is: where is the initial velocity in ft/sec of the object. What is the final velocity, v, of an object that slides down a frictionless inclined plane of height 2 feet with an initial velocity of 4 ft/sec? 7.1 nth Roots and Rational Expressions: Applications

Tuesday: Finish Puzzle worksheet Homework: Tuesday: Finish Puzzle worksheet Wednesday: Pg. 411-412 # 19, 20, 37-67 (odds) 7.1 nth Roots and Rational Expressions

From Math for Artists… “These are the laws of exponents and radicals in bright, cheerful, easy to memorize colors.” 7.1 nth Roots and Rational Expressions