Copyright © 2012 Pearson Education, Inc.  Publishing as Prentice Hall.

4.6

Square Roots and The Pythagorean Theorem

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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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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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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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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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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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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.