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5-7 Pythagorean Theorem and simplifying radical expressions Trigonometry Unit Radical Expressions Notes Radical expressions (definition) _____________________________________________ ______________________________________________________________________ Symbol___________ Perfect Squares________________________________________________________ _____________________________________________________________________ Simplify a radical expression 1)__________________________________________________________________ 2)__________________________________________________________________ 3)__________________________________________________________________ You know when an expression containing square roots is in simplest form when: 1)__________________________________________________________________ 2)__________________________________________________________________ 3)__________________________________________________________________ Example 1: Simplify 20 Example 2: Simplify 68 Example3: 20 * 20 Example 4: 128c6 Example 5: 3x 2 * 3 3x 4 Rationalize the denominator________________________________________ _______________________________________________________________ Example 6: 9 18 Example 7: 8 24 Pythagorean Triple Example 1: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. Example 2: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. Example 3: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. A set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2 is called a _____________________. The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths. Example 1: Using converse of the Pythagorean Theorem An entertainment center is 52 inches wide and 40 inches high. Will a television with a 50 inch diagonal fit in it? Explain. Tell if the measures 7, 11, and 15 can be the side lengths of a triangle. If so, is the triangle a right triangle?