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Chapter 11 Notes 11-1 Square Roots and Irrational Numbers perfect square – the answer when a number multiplied by itself example 3 x 3 = 9 9 is a perfect square square root – the number that when multiplied by itself equals the given number . the square root of 100 is 10 example 100 = 10 rational number – ratio, fraction – this is a number that can be written as a fraction including terminating decimals, and repeating decimals ¼ = 0.25 ⅓ = 0.333333 = 0.3 examples irrational number – the square root of a non perfect square a number that can not be written as a fraction examples 10 or = 3.141592538979323846264338327950288… To find the square root of a number that is NOT a perfect square, just find the square root of a perfect so 10 = 3 square that is CLOSE to the non-perfect square 9 = 3 Notes 11-2 Pythagorean Theorem hypotenuse – the longest side of a right triangle – it is opposite the right angle leg – a shorter side of a right triangle 2 2 2 Pythagorean Theorem – a + b = c The sum of the squares of the legs is equal to the square of the hypotenuse. example 32 + 42 = 52 102 + 112 ?= 122 9 + 16 = 25 100 + 121 ?= 144 25 = 25 yes 221 ≠ 144 no If given a leg, and the hypotenuse, to solve for the missing side, plug in and solve. If the hypotenuse is 5 and one side is 4, what is the remaining side? example a2 + 42 = 52 a2 + 16 = 25 – 16 – 16 2 a = 9 a2 = a = 3 9