Roots
The square root of a number is the nonnegative number whose square is the root. For example 3 is the square root of 9 because 32 = 9.
Examples
√16 = 4 because 42 = 16 √81 = 9 because 92 = 81
√625 = 25 because 252 = 625
It may seem
that negative numbers could be square roots. It is true that (-3)2 =
9. But √9 p is the symbol for
the nonnegative number whose square is 9. Sometimes we say that 3 is the principal square root of 9. When we speak
of an even root, we mean the nonnegative root. In general, 
if bn = a. There is no problem with
odd roots being negative numbers:
If n is even, b is assumed to be the
nonnegative root. Also even roots of negative numbers do not exist in the real
number system. In this book, it is assumed that even roots will be taken only
of nonnegative numbers. For instance in √x, it is assumed that x is not negative.
Root properties are similar to exponent properties.
Property 1 
We can take
the product then the root or take the individual roots then the product.
Examples
Property 1
only applies to multiplication. There is no similar property for addition (nor
subtraction). A common mistake is to ‘‘simplify’’ the sum of two squares. For
example 
is incorrect. The following example should
give you an idea of why these two expressions are not equal. If there were the
property
, then we would have:
This could
only be true if 102 = 58.
Property 2 
We can take
the quotient then the root or the individual roots then the quotient.
Property 3 
(Remember that if n is even,
then a must not be negative.)
We can take
the root then the power or the power then take the root.
Property 4 
Property 4
can be thought of as a root-power cancellation law.
Example
Practice
Solutions
“Sumber Informasi”
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