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Exploring Square Roots and the Pythagorean Theorem By: C Berg Edited By: V T Hamilton Perfect Square A number that is a square of an integer 2 Ex: 3 = 3 · 3 = 9 3 3 Creates a Perfect Square of 9 Perfect Square List the perfect squares for the numbers 1-12 Square Root The inverse of the square of a number Square Root Indicated by the symbol Radical Sign Square Root Example: 16 25 4 = 5 Square Root Estimating square roots of non-perfect squares Square Root Find the perfect squares immediately greater and less than the non-perfect square Square Root Example: 32 65 The answer is between 82 which is 64 and 92 which is 81 Pythagorean Theorem Pythagorean Theorem Formula to find a missing side of a right triangle Pythagorean Theorem ONLY WORKS FOR RIGHT TRIANGLES!!! Pythagorean Theorem Part of a Right Triangle: •Hypotenuse •2 Legs Pythagorean Theorem a= c = hypotenuse leg b = leg Pythagorean Theorem a= c = hypotenuse leg b = leg Pythagorean Theorem •Lengths of the legs: a&b •Length of the hypotenuse: c Pythagorean Theorem The sum of the squares of the legs is equal to the square of the hypotenuse Pythagorean Theorem 2 a + 2 b = 2 c Pythagorean Theorem 52 32 5 3 4 42 32 + 42 = 52 9 + 16 = 25 25 = 25