copyright © 2012 pearson education, inc. publishing as prentice hall. 4.6 square roots and the...
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
4.6
Square Roots and The Pythagorean Theorem
22
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Finding Square Roots
Square Root of a Number
A square root of a number a is a number b whose square is a. We use the radical sign to name square roots. In symbols,
2 if
Also,
0 0
a b b a
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Find each square root.
a.
b.
c.
281 9 because 9 81
1 1 1 1 1 because
25 5 5 5 25
9 3 3 3 9 because
64 8 8 8 64
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Approximate each square root to the nearest thousandth.
a.
b.
c.
58 7.616
13 3.606
89 9.434
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Using the Pythagorean Theorem
Pythagorean Theorem
In any right triangle,
(leg)2 + (other leg)2 = (hypotenuse)2
hypotenuseleg
leg
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Using the Pythagorean Theorem
Finding an Unknown Length of a Right Triangle
2 2
2 2
hypotenuse = leg other leg
or
leg = hypotenuse other leg
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Find the length of the hypotenuse of the given right triangle.
48 m
22 m
2 2
2 2
hypotenuse = leg other leg
hypotenuse = 22 48
484 2304
2788
52.802
The hypotenuse is approximately 53 meters long.
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Find the length of the leg of the given right triangle.
3 yd
9 yd
2 2
2 2
leg = hypotenuse other leg
leg = 9 3
81 9
72
8.485
The leg is approximately 8 yards long.