3
@12 Simplifying
%3
^1
The square root of a number is one 
of its two equal factors.  The 
principal square root is a positive
number. The principal square root 
of 36 is 6.
^2
To simplify a square root, factor the 
radicand (the number inside the 
radical).  
Use a perfect square (4, 9, 16,
 25, ...) for one of the factors.
^3
Remove the perfect square factor by 
writing its principal square root in 
front of the radical sign.
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%5
^1
Every positive real number has two
square roots, one positive and one
negative.  The square root of 49 is
+7 or -7.
^2
To simplify a square root that involves 
variables, first factor the numerical 
coefficient using a perfect square.
^3
If the exponent is odd, separate the 
power into two factors.  Use the 
largest possible even exponent as one 
factor.
^4
Then remove the perfect square 
numerical factor by writing its square 
root in front of the radical. 
^5
Finally, take the square root of the 
even powers.  (Divide the exponents by 
2.)
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@22 Multiplying and Dividing
%5
^1
When multiplying radical expressions, 
multiply the coefficients and the 
radicands separately.
^2
First, multiply the coefficients; then, 
multiply the radicands. 
^3
Factor the radicand using a perfect 
square.
^4
Remove the perfect square factor by 
writing its square root in front of the 
radical.
^5
Simplify.
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%3
^1
A radical expression in simplest form 
cannot have a radical in the denominator. 
^2
To "rationalize the denominator," 
multiply both terms of the fraction by 
the radical in the denominator.
^3
Simplify, noting that any radical times 
itself (squared) equals the radicand.
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@32 Adding and Subtracting
%2
^1
Radical expressions may be added and 
subtracted only if their radicands are 
alike.  
^2
Combine the coefficients of like 
radicands as one term.
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%3
^1
Radical expressions may be added and 
subtracted only if their radicands are 
alike.  
^2
Simplify all radical expressions by 
taking the square root of perfect 
square factors.
^3
Combine the coefficients of like 
radicands as one term.
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