Roots-and-Radicals

Unit 8 - Roots & Radical Expressions
Big ideas:
 * [|Essential Topics: Roots & Radical Expressions]
 * when you have a fractional exponent, you can split it up
 * ex) 25^(3/2) = (25^1/2)^3 = (sqrt25)^3 = 5^3 = 125
 * when you have (A^3 - B^3) or (A^3 + B^3) SOAP helps
 * s - sometimes pos., sometimes neg (or same as the sign in the cubed unfactored polynomial)
 * o - opposite of whatever the s turns out to be
 * ap - always positive
 * to avoid losing points by forgetting an absolute val. put an absolute value around the whole final answer! its cheap but it works.
 * when you have a fraction with "i" multiply by the conjugate to simplify
 * the conjugate is the expression of the denominator with the opposite sign ( + or - )
 * when you have a function operation like (g °f)(x) that means g of f(x)
 * ex) (g °f)(x) when g(x) = 2x and f(x) = x^2 + 4 would be (2x)^2 + 4 :)
 * domain for the above example is all real numbers!

Helpful hints:
 * something is a function if it passes the vertical line test!
 * the inverse of a function is a function if the original function passes the horizontal line test
 * when you take the inverse of a function, range of the original becomes domain of the inverse and vice versa
 * to graph an inverse, flip it over y=x
 * when you have an inequality with multiple factors, use the number line graph to solve for x
 * ex) (2x - 2) / (x - 1) < x+1
 * factor it and get 0 > (x-3)(x+1)/ (x-1)
 * split up a number line into 4 sections (3 separating lines at 3, -1, 1)
 * multiply the signs for each section to get the signs and then get the domain.

Sample Problems: (click here for solutions to these problems)
 * 1) calculate 256 ^ 1.25 robert w
 * 2) Simplify the following:square root of 75 + square root of 100 -Bailey
 * 3) Simplify: (-125)^(2/3)
 * 4) Solve: sqrrt(75) + sqrrt(3x)= 12*sqrrt(3)
 * 5) Using the rational root theorem and synthetic division, find the roots of 3x^3 + 12x^2 - 3x - 12 = y. - Caroline
 * 6) graph the equation y = x^ (2/5)
 * 7) Simpifiy:(x^8 * y^-2)/ (x^2 * y^6)
 * 8) solve (5-x)^.5 = x + 1 for x and check for extraneous solutions robert w