8.1Square Roots and the Pythagorean Theorem
Square RootSquare Root
Square RootSquare Root
ExampleExampleFind each square root.a.
b.
c.
d.
e.
f.
g.
h.
Approximating Square RootApproximating Square RootThe period of a pendulum is the time required for the pendulum to swing back and forth to complete one cycle.
The period t (in seconds) is a function of the pendulum’s length l (in feet), which is defined by t = f (l ) = 1.11
Find the period of a pendulum that is 5 feet long.
Example – Example – SolutionSolutionWe substitute 5 for l in the formula and simplify.
t = 1.11
= 1.11 1.11 (2.24) 2.48
The period is approximately 2.5 seconds for a 5-foot-long pendulum.
Rational, Irrational, or Rational, Irrational, or ImaginaryImaginary
Imaginary NumberImaginary Number
ExampleExampleDetermine whether the following are
rational, irrational, or imaginary.a.
b.
c.
ExampleExampleGraph: Solution:To graph this function, we make a table of values and plot each pair of points.
Pythagorean TheoremPythagorean TheoremGiven a right triangle:
Hypotenuse is the side opposite the right angle and is the longest side. Legs of the (right) triangle are the other 2 sides.
Pythagorean Theorem:
c2 = a2 + b2
Example – Example – Building A High-Ropes Building A High-Ropes Adventure CourseAdventure Course
The builder of a high-ropes course wants to stabilize the pole shown by attaching a cable from a ground anchor 20 feet from its base to a point 15 feet up the pole. How long will the able be?
Example – Example – Building A High-Ropes Building A High-Ropes Adventure CourseAdventure Course
Your TurnYour Turn
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