Equations
can be used to
calculate the
square root of
a
number.

Simplify
the Square
Root
Calculation.
To
simplify
the square
root
calculation:
1)
Factor
the
radicand
into
a series
of
perfect
squares
2)
Evaluate
the square
root of
each
perfect
square
separately

thus
removing
every
perfect
square
from
beneath
the square
root
radical.
3)
Once the
perfect
squares
have been
removed
from
beneath
the square
root
radical,
evaluate
the
surd
(the
remaining,
unevaluated
square
root)
using
standard
methods
such as
Newton's
Method,
Direct
Calculation,
a Square
Root
Table, or
the Guess
& Check
Method.
4)
Multiply
all the
results
obtained
separately
(in steps
2 & 3).
Skip to
example 
click
here
Simplify
a Square Root
Calculation 
free ONLINE
Calculator
Compute a
simplified
square root for
any number.
Practice
simplifying a
square root
radical, and
check your work
using these
online
calculators:
http://www.mathwarehouse.com/arithmetic/squarerootcalculator.php
http://www.webmath.com/simpsqrt.html

Factor the
Square
Root
Equation
Equations
can be
used to
evaluate
square
roots by
setting
the
equation
equal to
zero, then
factoring
the
equation.
This
method
works well
for
numbers
which are
perfect
squares,
but is
very
difficult
to use
when
calculating
the square
root of a
number
which is
not a
perfect
square.
However,
factoring
has the
advantage
of
identifying
both
positive
and
negative
roots.
Skip to
example 
click
here
Compute a
Square Root by
Factoring the
Square Root
Equation  free
ONLINE
Calculator.
Practice
factoring a
square root
equation, and
check your work
using these
online
calculators:
http://www.algebrahelp.com/calculators/equation/factoring/
http://www.freemathhelp.com/factoringcalculator.php
http://www.basicmathematics.com/factoringcalculator.html
Calculate
Square Root . .
.
using
equations
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Example

Simplify
the Square Root
Calculation
Factor the
radicand into a
series of
perfect squares
(to the maximum
extent
possible).
Calculate
Square
Root:
Step
1:
Factor
the radicand
into
a series of
perfect
squares.
Step
2:
Evaluate
the square root
of each
perfect square
separately
 thus
removing every
perfect square
from beneath
the square root
radical.
Note:
while each
square root has
two solutions
(+ and ), it
is only
necessary to
show the
positive values
in this
step.
Step
3:
Evaluate
the remaining
SURD
. Once the
perfect
squares
have been
removed
from
beneath
the square
root
radical,
evaluate
the surd
(the
remaining,
unevaluated
square
root)
using
standard
methods
such as
Newton's
Method,
Direct
Calculation,
a Square
Root
Table, or
the Guess
& Check
Method.
Step
4:
Multiply
all the
results
obtained
separately
(in steps 2 &
3).
The
final answer
is:
to 4
decimal
points
Example

Rewrite
the equation in
standard
quadratic
form.
Solve the
quadratic
equation to
find the
roots.
Calculate
Square
Root:
Step
1:
Square
each side
of the
equation.
Step
2:
Rewrite
the equation
shown in step 1
in standard
quadratic
form.
Step
3:
Factor
the quadratic
equation.
Step
4:
Using
the
ZeroProduct
Principle, set
the first
factor
equal to zero,
then solve for
x.
(The
ZeroProduct
Principle
states that
when two
factors
multiplied
together equal
zero, either
one factor or
both factors
must equal
zero.)
Step
5:
Set the
second
factor
equal to zero,
then solve for
x.
The
final answer
is:
(The
square root has
a different
solution for
each
factor.)