Square Root Property
The __square root
property__ is one method that is used to find the solutions to a
quadratic (second degree) equation. This method involves taking the square roots of both sides of
the
equation. Before taking the square root of each side, you must isolate
the term that contains the squared variable. Once this squared-variable
term is fully isolated, you will take the square root of both sides and
solve for the variable. We now introduce the possibility of two roots for
every square root, one positive and one negative. Place a _{} sign in front of the side containing the constant
before you take the square root of that side.
Example 1:
_{}
the squared-variable term is isolated, so we
will take the square root of each side
_{}
notice the use of the _{} sign, this will give us both a positive and
a negative root
_{}
simplify both sides of the equation, here x
is isolated so we have
solved this equation
Example 2:
_{}
again the squared-variable term is
isolated, so we will take the
square root of each side
_{}
again dont forget the _{} sign, now simplify the radicals
_{}
this time p is not fully
isolated, also notice that _{}4 are rational
numbers, which means
_{} and _{}
_{} and _{}
Example 3:
_{}
squared term is not isolated, add 1
to each side before beginning
_{}
now take the square root of both sides
_{}
simplify radicals
_{}
radical containing the constant cannot be
simplified, solve for the variable
_{}
notice the placement of the 1 before the
radical on the right-hand
side, these numbers may not be combined since 1 is a rational
number and _{} are irrational numbers
_{}
_{}
_{}
In each of the (above) 3
examples involving the square root property, notice that there were no
first-degree terms. These equations although they are quadratic in
nature, have the form
_{}or
_{}
**
General Algebra Tips**
The views and
opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia
State Community College. This page was
edited on
15-Nov-2007 |