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4.6-Square Roots and the Pythagorean Theorem CATHERINE CONWAY MATH081

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Perfect Square A number that is a square of an integer Ex: 3 2 = 3 · 3 = 9 3 3 Creates a Perfect Square of 9

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Perfect Square List the perfect squares for the numbers 1-12

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Square Root The inverse of the square of a number Indicated by the symbol Radical Sign

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Square Root Example: = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9

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Practice Simplify the following expression without using a calculator

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Square Root Estimating square roots of non-perfect squares Find the perfect squares immediately greater and less than the non-perfect square Example:

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Approximations for the square root of 7

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Pythagorean Theorem

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Formula to find a missing side of a right triangle a 2 + b 2 = c 2 ONLY WORKS FOR RIGHT TRIANGLES!!!

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Pythagorean Theorem Part of a Right Triangle: Hypotenuse 2 Legs a = leg b = leg c = hypotenuse

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Pythagorean Theorem a = leg b = leg c = hypotenuse The corner of the square always points to the hypotenuse

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Pythagorean Theorem Lengths of the legs: a & b Length of the hypotenuse: c The sum of the squares of the legs is equal to the square of the hypotenuse a 2 + b 2 = c 2

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Pythagorean Theorem 3 3232 4242 5252 4 5 3 2 + 4 2 = 5 2 9 + 16 = 25 25 = 25

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Using the Pythagorean Theorem Find the length of the hypothenuse, c, for the right triangle with sides, a = 6 and b = 8 Find the length of the hypothenuse, c, for the right triangle with sides, a = 12 and b = 16 a 2 + b 2 = c 2 12 2 + 16 2 = c 2 144 + 256 = c 2 400 = c 2 20 = c a 2 + b 2 = c 2 6 2 + 8 2 = c 2 36 + 64 = c 2 100 = c 2 10 = c

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