Download Simplifying Radicals (power point)

Simplifying Radicals
Perfect Squares
1
64
225
4
81
256
9
16
100
121
289
25
36
49
144
169
196
400
324
625
4
=2
16
=4
25
=5
100
= 10
144
= 12
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
8
=
4*2 =
2 2
20
=
4*5
=
2 5
32
=
16 * 2 =
4 2
75
=
25 * 3 =
5 3
40
=
4 *10 = 2 10
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
48
=
16 * 3 =
4 3
80
=
16 * 5 =
4 5
50
=
25 * 2 = 25 2
125
=
25 * 5 =
450
=
225 * 2 = 15 2
5 5
+
To combine radicals: combine
the coefficients of like radicals
Simplify each expression
6 7 5 7 3 7 
8 7
5 6 3 7 4 7 2 6 
3 6 7 7
Simplify each expression: Simplify each radical first and
then combine.
2 50  3 32  2 25 * 2  3 16 * 2 
2 *5 2  3* 4 2 
10 2  12 2 
2 2
Simplify each expression: Simplify each radical first and
then combine.
3 27  5 48  3 9 * 3  5 16 * 3 
3*3 3  5* 4 3 
9 2  20 2 
29 2
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
18
=
=
288
=
=
75
=
=
24
=
=
72
=
=
Simplify each expression
6 5 5 6 3 6 
3 24  7 54 
2 8  7 32 
Simplify each expression
6 5  5 20 
18  7 32 
2 28  7  6 63 
*
To multiply radicals: multiply the
coefficients and then multiply
the radicands and then simplify
the remaining radicals.
Multiply and then simplify
5 * 35  175  25 * 7  5 7
2 8 * 3 7  6 56  6 4 *14 
6 * 2 14  12 14
2 5 * 4 20  20 100  20 *10  200
 5
2

5* 5 
25 

7* 7 
49  7

8* 8 
64  8

x* x 
x 
 7
2
 8
2
 x
2
2
5
x
X
Y
4
2
=X
= Y3
6
6
2
P X Y
4
4X Y
8
2
= P2X3Y
= 2X2Y
10 =
25C D
5C4D10
X
3
=
X
=
Y
5
2
X
*X
X
=
Y
=
2
Y
4
Y
Y
3
PX Y
3
=
2
X Y
= XY
7
12 X Y
8
2
=
Y
9
25C D =
Y
5
5
2
* PXY
PXY