6.3 Simplifying Radical Expressions

1
6.3 Simplifying Radical Expressions
2
n a n b n ab Indices n have to match

• 6 4 6 5
• x 3 x 3
• 3 16 3 y
• x 2

3
n a n b n ab Indices n have to match

• 6 4 6 5
• 6 20
• x 3 x 3
• x2 9
• 3 16 3 y
• x 2
• 3 16y 3 8y 2 3 y
• 2x x x

4
Factoring

• n ab n a n b
• Find 2 numbers with one of them is the largest
  perfect nth power

5
Example 1

• 20
• 4 5
• 2 5

6
Example 2

• 3 200
• 3 825
• 3 8 3 25
• 2 3 25

Or factor 200 200 2 100 2 2 50
2 2 2 25 23 52
3
23 52 2 25
3
7

• 432x5y3
• 12 3x5y3
• 12 3x4 x y2 y
• 12x2 y 3 x y

• 432 2 216
• 2 2108
• 22 2 54
• 222227
• 222293
• 2222333
• 22 22 32 3
• 432 2 23 3
• 12 3

8

1. 5 32xy10
2. 2x2 4xy 2y2
3. 3 x7y9z11
4. 18x9y5z6

9

• 5 32xy10 2y2 5 x
• 2x2 4xy 2y2 2(x2 2xy y2)
• 2(xy) 2 xy
  2
• 5) 3 x7y9z11
• x2y3z3 3 xz2
• 18x9y5z6 9 2x9y5z6 3x4y2z3 2xy

10

• 7) 2 4 8x3y5 (-3) 4 4x2y3
• 8) 5 a3 (b-c) 4 5 a7 (b-c)9

11

• 7) 2 4 8x3y5 (-3) 4 4x2y3
• -6 4 32x5y8
• -6 4 216x5y8
• -6(2) xy2 4 2x
• -12xy2 4 2x
• 8) 5 a3 (b-c) 4 5 a7 (b-c)9
• 5 a10 (b-c)13
• a2 (b-c)2 5 (b-c)3

Assume that we have all positive numbers
12
n a n a b n b

• 3 27
• y6z2

• 16x 3
• y10

13
n a n a b n b

• 3 27
• y6z2
• 3 27
• 3 y6z2
• 3
• y2 3 z2

• 16x 3
• y10
• 42 x 3
• y10
• 4x x
• y5

14
n a n a n b
b

• 72xy
• 2 2x2

• 2) 5 3 32
• 3 2

15
n a n a n b
b

• 72xy
• 2 2x2
• 1 72xy
• 2 2x2
• 1 36y
• 2 x
• 6 y 3 y
• 2 x x

• 2) 5 3 32
• 3 2
• 5 3 16
• 5 3 82
• 52 3 2
• 10 3 2

16
n a n a n b
b

• 3) 4 x3
• 3 x2