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Transcript
Exploring Square Roots and the Pythagorean Theorem 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 Pythagorean a +b =c Theorem 2 2 2 152 + 202 = c2 225 + 400 = c2 c 15 ft 20 ft √625 = 25 Pythagorean a +b =c Theorem 6 + b = 12 2 2 2 2 2 2 36 + b2 = 144 -36 b 6 ft -36 2 =108 b √108 = 10.39 12 ft