Chapter+11

11.1 Simplify Radical Expressions The square Root of ab= square root of a,and square root of b if they are greater than zero. We broke it down to simplify it. 1. Prime factorization 2.combine x^2 3. take the sqrt of parts you can 4. simplify If varible is outside the square root symbol is negative has no absolute symbol, if the exponent is odd it has to have an absolute vaule symbol. 1. divide numbers then find the square root of that number. 2. Break up the numbers and find the square root of each number getting ride of the one on the bottom multiply that. the multiply across. When their is subtraction you can not simply multiply by the bottom. you need to do the entire bottom not just 1 number. Subtraction 1.Write problem 2. Multiply by a fraction equal to one start with (-) change to +. 3.Multiply numerators 4. Multiply denominators 5. Simplyfy numerators 6. Simplyfy denominator 7. reduce fractionif needed. 11.2 Operations with radical expressions (problems with square roots in them) Adding 3 square root of 2+ 4 square rootof 2= 7 sqaure root of 2 Can not simplify unless radical is identical. Subtracting Same as adding just subtract Can not simplfiy unless radical is the same. Multiplying (FOIL)

10.3 Extraneous Solutions Square root of -k=4 1. square both sides = -k=16 make k= -16 3*square root of 7 = square root of -y 1. square root9 9*7= If you end up with a negative number in you solution ste thats you extraneous solution.

11.4 Pythagorean Theorem only works forright triangles formula a^2+b^2=c^2 or c^2-a^2=b^2 or c^2- b^2=a^2 Pythagororean triples if you have a 3,4 on a triangle the hypotonuse=5 If you have a 6, 8, 10 =10 leg-2 leg a, and b it doesnt mattewr which one is which, the legs make up trhe right angle hypotenouse- always c

11.5 Distance formula square root (x2-x1)^2-(y2-y2)^2 When looking for distance answer must be positive. when looking for missing x or y value its ok 2 have more than 1 answer. 1.wrote problem 2. filled in varibles 3. simplifyed 4. squared both sides 5.made 1 side equal to zero 6. factored 11.6 Similar Triangles- same shape not same size can be used reducing or enlarging ratio

11.7 soh= oppisite/hypotoneous cah=adjacent/hypotonuese tan=oppisite/adjacent