5-7 Pythagorean Theorem and simplifying radical expressions
Trigonometry Unit
Radical Expressions Notes
Radical expressions (definition) _____________________________________________
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Symbol___________
Perfect Squares________________________________________________________
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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________________________________________
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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?