The Pythagorean theorem states that in any right triangle with perpendicular sides
aand band longest side c,
It is used in surveying, drafting, engineering, navigation, and many other fields.
Although attributed to Pythagoras, it was known to surveyors from Egypt to China for
a thousand years before Pythagoras.
In the 1939 movie The Wizard of Oz,the Scarecrow asks the Wizard for a brain.
When the Wizard presents him with a diploma granting him a Th.D. ( Doctor of
Thinkology), the Scarecrow declares the following.
The sum of the square roots of any two sides of an isosceles triangle is equal to
the square root of the remaining side.... Oh joy! Rapture! I’ve got a brain.
Did the Scarecrow state the Pythagorean theorem correctly? We will investigate this
in Exercises 133 – 134of Section 8.3.
a^2 +b^2 =c^2.
Roots, Radicals,
and Root Functions
8.1 Radical Expressions and Graphs
and Graphs
8.2 Rational Exponents
8.3 Simplifying Radical Expressions
Expressions
8.4 Adding and
Subtracting Radical
Expressions
8.5 Multiplying and
Dividing Radical
Expressions
Summary Exercises on
Operations with Radicals
and Rational Exponents
8.6 Solving Equations with Radicals
with Radicals
8.7 Complex Numbers
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CHAPTER