8.1 Square Roots and the Pythagorean Theorem. Square Root.
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Transcript of 8.1 Square Roots and the Pythagorean Theorem. Square Root.
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