Algebra II Honors—Day 13

Warmup Pick up the handouts on the table. Do as many of the “Perfect Squares” on the back as you can in 1 minute. Then try the “Non-Perfect Squares” WITHOUT A CALCULATOR. I’m looking for the simplest radical form—not the decimal approximation.

Goals for Today Second Graded Homework Assignment (checked for accuracy)—due Monday, Sept. 16—5-point bonus if turned in on Friday, Sept. 13 Essential Questions/New Material Homework

Essential Questions How do I evaluate roots of real numbers? How do I rewrite roots of real numbers as rational expressions?

Notes Review from Algebra I—definitions A term like is called a “power” The “3” is the coefficient “x” is the base “2” is the exponent

Review Laws of Exponents When you multiply like bases, add the exponents. Example: Add the exponents. Keep the base.

Review Laws of Exponents When you raise a power to a power, multiply exponents. means This is the same as or

Review Laws of Exponents When you divide powers with the same bases, subtract the exponents. means Cancel out common factors on top and bottom. This leaves which is the same as

More Exponent Info Graphic Organizer for Exponents

New stuff Radical—an expression with a root symbol If the index is even and the radicand is positive, there are two roots—one positive and one negative. If the index is even and the radicand is negative, there are no real roots—only complex ones. INDEX RADICAND

Rational Exponents What if the exponent is a rational number instead of an integer??? EXAMPLE: What does or mean? I’ll write out these notes today under the document camera.

Homework Handout on Radicals and Rational Exponents