Square Roots and the Pythagorean Theorem

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Square Roots and the Pythagorean Theorem
Section 6.4
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The square of a number is the number times itself.
The square of 6 is 36 because .
The square of - 6 is also 36 because
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The reverse process of squaring is finding a
square root.
A square root of 36 is 6 because .
A square root of 36 is also 6 because

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Square Root of a Number
0.
Also,
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Helpful Hint
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Numbers like are
called perfect squares because their square
root is a whole number or a fraction.
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Approximating Square Roots
A square root such as cannot be written as
a whole number or a fraction since 6 is not a
perfect square. It can be approximated by
estimating, by using a table, or by using a
calculator.
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One important application of square roots has to
do with right triangles.
A right triangle is a triangle in which one of
the angles is a right angle or measures 90º
(degrees).
The hypotenuse of a right triangle is the side
opposite the right angle.
The legs of a right triangle are the other two
sides.
hypotenuse
leg
leg
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Pythagorean Theorem
If a and b are the lengths of the legs of a
right triangle and c is the length of the
hypotenuse, then
In other words,
(leg)2 (other leg)2 (hypotenuse)2.
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