Irrational Numbers 11-6 The Pythagorean Theorem
The Pythagorean Theorem In any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs. a 2 + b 2 = c 2
Example a c b
8 c 15
Solution a 2 + b 2 = c = c =c =c 2 17 = c
Example The length of one side of a right triangle is 28 cm. The length of the hypotenuse is 53 cm. Find the length of the unknown side.
Solution a 2 + b 2 = c 2 a = 53 2 a =2809 a 2 =2025 a = 45
Converse of the Pythagorean Theorem If the sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest, then the triangle is a right triangle. The right side is opposite the longest side.
Radical Expressions 11-7 Multiplying, Dividing, and Simplifying Radicals
Rationalization The process of eliminating a radical from the denominator.
Simplest Form No integral radicand has a perfect-square factor other than 1 No fractions are under a radical sign, and No radicals are in a denominator