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Chapter 11 Review

Chapter 11 Review. 11-1 Simplifying Radicals. To simplify a radical, find numbers that multiply to give you the number that you are trying to simplify You always want to get it to prime numbers If you find a pair, then the couple comes out of the “house”, the “lone wolves” stay in the “house”

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Chapter 11 Review

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  1. Chapter 11 Review

  2. 11-1 Simplifying Radicals • To simplify a radical, find numbers that multiply to give you the number that you are trying to simplify • You always want to get it to prime numbers • If you find a pair, then the couple comes out of the “house”, the “lone wolves” stay in the “house” • If you have multiples then they get multiplied • If you have variables included the same rules apply • When you are multiplying radicals you can multiply radicals, however you cannot multiply number outside of the radicals with number inside the radicals • When you have fractions, simplify the fractions before you simplify the radical • You may have to rationalize the denominator before you simplify the radical • Practice problems Page 619 1-24all, 28-51all, 57-71all

  3. 11-2 Operations with Radical Expressions • You can only add/subtract like radicals • You may have to simplify radicals so that they are like. You do this the same way you did in section 11-1 • When you have parenthesis you have to use the distributive property to get rid of the parenthesis and simplify the expression. Remember that if you are multiplying two radicals then the number under the radicals can be multiplied, however if one number is outside and one number is inside then they must remain like that. • If you have two binomials then you have to use FOIL to simplify them. Use it just like any other binomials • Remember that you cannot have any radicals in the denominator. If you do and there is an addition or subtraction sign you must use the conjugate to remove the radicals. Square both numbers and ALWAYS put a subtraction sign in between the two numbers you come up with. • Practice problem Page 625 1-6all, 10-36all, 38-46all

  4. 11-3 Solving Radical Equations • When you are solving radical equations, you must always isolate the radical on one side of the equal sign. • Once you have done that, then square both sides of the equations. • Solve for the variable. Always make sure that you check your solution. • Both, one or neither of the solution may work. You may have an extraneous solution (one that does not work) • Practice problem Page 632 1-6all, 9-28all, 34-43all

  5. 11-5 Trigonometric Ratios • You can only use trig functions on right triangles • Sin = opp/hypsohcahtoa • Cos = adj/hyp • Tan = opp/adj • If you are trying to find an angles then you use the trig function inverse (-1 exponent) • Practice problems Page 648 1-24all, 26-33all

  6. 11-6 Angles of Elevation & Depression • You use trig functions to calculate the sides or angles that you are missing, based on the information given and the point of view given. • It is a lot easier because the lines are parallel so that you can use alternate interior angles, to find the measurement of the angles you can use. • Then you have to decide what trig function you are going to use & use it. • Practice problems Page 652 1-10all

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