Simplifying Radicals. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400...
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Transcript of Simplifying Radicals. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400...
Look at these examples and try to find the pattern…
How do you simplify variables in the radical?
x7
1x x2x x3x x x4 2x x5 2x x x6 3x x
What is the answer to ? x7
7 3x x x
As a general rule, divide the exponent by two.
The remainder stays in the radical.
8
20
32
75
40
=
= =
=
=
2*4
5*4
2*16
3*25
10*4
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
48
80
50
125
450
=
= =
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
87
249
5010
125
453
=
= =
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
18
288
75
24
72
=
= =
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
Simplify each expression: Simplify each radical first and then combine.
485273
229
22029
34*533*3
3*1653*93
18
288
75
24
72
=
= =
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
*To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.
To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator
7
6This cannot be
divided which leaves the radical in the
denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
42 cannot be simplified, so we are
finished.
This can be divided which leaves the
radical in the denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
10
5
This cannot be divided which leaves
the radical in the denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
12
3
This cannot be divided which leaves
the radical in the denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
20
5
Look at these examples and try to find the pattern…
How do you simplify variables in the radical?
x7
1x x2x x3x x x4 2x x5 2x x x6 3x x
What is the answer to ? x7
7 3x x x
As a general rule, divide the exponent by two.
The remainder stays in the radical.
Look at these examples and try to find the pattern…
How do you simplify variables in the radical?
2x x
4 2x x
6 3x x
As a general rule, divide the exponent by two.