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
It may seem that negative numbers
could be square roots. It is true that (–3)2 = 9. But √9 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:
because (–4)3
= (–4)(–4)(–4):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.
Examples
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.
Examples
Sumber
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