Multiplication of radicals
18
Click here to load reader
Transcript of Multiplication of radicals
Multiplication of Radicals
MATHEMATICS REWIND
Add the following radicals
β’ 34 , 48
4
β’ 52
, 62 , 20
2, 2942
β’ π₯43
+ π₯73
Multiplication of Radicals
Three cases of multiplications of radicals
β’ Same indices β’ Different indices but same radicand β’ Totally different in indices and
radicands
First case: Same indices
β’ π₯π β π¦π = π₯π¦π
Examples
β’ 34
β 44
β’ 3 β 44
β’ 124
β’ 105
β 25
β’ 10 β 25
β’ 205
Boardwork:
β’ 105
β 205
β’ 166
β 46
β’ 128007
β 10007
β 1007
Practice exercise
β’ Simplify the following radicals:
β’ ( 64
β 104
)( 94
β 104
)
β’4
3β 163
2
β’ Show that the product of the roots of a quadratic equation is
π
π.
Second case: Different indices same radicand
β’ πππ₯
β πππ¦
β’ ππ
π₯ β ππ
π¦
β’ πππ¦
π₯π¦ β πππ₯
π₯π¦
β’ πππ¦+ππ₯
π₯π¦
β’ πππ¦+ππ₯π₯π¦
Example
β’ 52
β 53
β’ 51
2 β 51
3
β’ 53
6 β 52
6
β’ 55
6
β’ 31256
Boardwork
β’ Simplify the following expressions:
β’ 84
β 85
β’ π₯710
β π₯720
β’ π¦π₯ β π¦π§
Practice Exercise
β’ Simplify the following to simplest radical form. Show the step-by-step solution
β’ 1. 63
β 62
β 64
β’ 2. ( π2 + π2)( π2 + π23
)
β’ 3. 72 β 163
Case 3: Totally Different
β’ πππ₯
β πππ¦
β’ ππ
π₯ β ππ
π¦
β’ πππ¦
π₯π¦ β πππ₯
π₯π¦
β’ πππ¦ β πππ₯π₯π¦
Example
β’ 43
β 52
β’ 41
3 β 51
2
β’ 42
6 β 53
6
β’ 42 β 536
β’ 20006
Boardwork
β’ Simplify the following:
β’ 53
β 22
β 74
β’ π₯10 β π₯92015
(kudos to who will answer this)
Practice exercise
β’ Simplify the following expressions:
β’ π2 β 3π3
β’ ( π2 + π2)( π2 β π23
)
