|
 for
all real numbers
 if
both x and y
are non-negative, and
 if
both x and y
are non-negative, and y
is not zero
WARNING:
Never cancel something inside
a radical with something outside
of it:
WRONG! If you did this
you would be canceling a 3
with ,
and they are certainly not
the same number.
The
general plan for reducing
the radicand is to remove
any perfect powers. We are
only considering square roots
here, so what we are looking
for is any factor that is
a perfect square. In the following
examples we will assume that
x is positive.
Example:
In
this case the 16 was recognized
as a perfect square and removed
from the radical, causing
it to become its square root,
4.
Example:
Although
x3 is not
a perfect square, it has a
factor of x2,
which is the square of x.
Example:
Here
the perfect square factor
is x4, which
is the square of x2.
Example:
In
this example we could take
out a 4 and a factor of x2,
leaving behind a 2 and one
factor of x.
·
The basic idea
is to factor out anything
that is “square-rootable”
and then go ahead and square
root it. |
