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Simplifying Variable Radicals
Contributed by: Smith
x2 * x2 =  x4
x3 * x3 =  x6
x4 * x4 =  x8
x  * x  =  x2
Perfect Squares
Continue the pattern...
Perfect squares with
a variable base (like x),
have ________ powers.
EVEN
 ODD
Perfect squares with a variable base (like x),                  have EVEN powers.
x2
x7
Click on ALL perfect Squares
x3
x8
x5
x20
x42
x6
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
√
x6
x3
x7
√
√
x
x
√
√
√
x10
x4
?
x16
=
=
=
x5
?
x8
?
x2
?
DRAG
THE 
TERMS 
BELOW
TO THE
RIGHT
SPOTS
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x12
√
x
x13
√
√
x
x
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x14
√
x
x15
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x
√
x
x21
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x
√
x47
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x
√
x19
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x
√
x25
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x
√
x49
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
x
√
x43
√
√
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a4x2
a8x4
√
a8x5
√
√
x
x
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a  x
a  x
√
a6x9
√
√
x
x
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a  x
a  x
√
a10x5
√
√
x
x
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a  x
a  x
√
a17x9
√
√
ax
ax
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a  x
a  x
√
a7x31
√
√
ax
ax
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a  x
a  x
√
a5x41
√
√
ax
Simplify the
perfect square.
Bring down the
imperfect square:
Rewrite
using the
GREATEST
perfect square
factor:
Simplify:
√
a  x
a  x
√
a29x25
√
√
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