Finding Square Roots

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Finding Square Roots
-a number a is a square root of b if a2
b Example 42 16 and (-4)2 16, so 4 and -4
are square roots of 16 -a radical symbol
indicates a square root. The expression under
the radical sign is a radicand.
Example 1 Simplify the following square
roots. a.) b.) c.) d.)

8
-3/5
Is undefined
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-Some square roots are rational numbers and some
are irrational. Example Rational Irrational
-1.2, 9, 2/3 .57734, -2.1348274
Example 2 Tell whether each expression is
rational or irrational. a.) b.)
irrational
rational
Estimating Square Roots
-The squares of integers are called perfect
squares. Consecutive Integers 1 2 3 4 5 6 7 Perfe
ct Squares 1 4 9 16 25 36 49 -You can estimate
square roots by using perfect squares.
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Example 3 Estimate the following square roots by
asking yourself which two perfect squares is the
radicand in between. Between what two
consecutive integers are the following. a.) b.
)
105 is between the two perfect squares 100 and 121
14.52 is between the two perfect squares 9 and 16
Therefore,
Therefore,
Is between 3 and 4
Is between -10 and -11
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Example 4 Approximate the following square roots
using a calculator. a.) b.)
-14.25
4.22
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Factoring Square Roots
Factoring square roots is just like factoring any
integer, but our goal is to find factors that
are perfect squares.
Example of Factoring an Integer 24 8 x 3
4 x 2 2 x 2
So 24 2 x 2 x 2 x 3
Example of Factoring a Square Root
So,
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Example 5 - Factor these square roots into
simplest form. a.) b.)