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

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