Menyederhanakan akar
Presentation
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
Jemi Hari Puryanto
Used 1+ times
FREE Resource
6 Slides • 0 Questions
1
Ngawi
𝟓𝟒
𝟖
𝟗𝟔
𝟏𝟐 + 𝟐 𝟒𝟖
𝟔 𝟔 𝒙 𝟑 𝟏𝟐
𝟑 𝟐𝒙𝟒 𝟐𝟒
𝟏𝟖
2
Ngawi
Dari Sifat perpangkatan
(
𝒂
𝒙
𝒃
)
𝒏
=
𝒂
𝒏
𝒙
𝒃
𝒏Maka berlaku juga
Misalkan
𝒄
Bisa disederhanakan jika
𝒄
=
𝒂
𝒙
𝒃
Bilangan kuadrat sempurna
4, 9, 16, 25, 36, ......
CONTOH
𝟏𝟐
=
𝟒
𝒙
𝟑
Dengan c bil Asli
𝟒
𝒙
𝟑
=
𝟐
𝟑
=
𝟓𝟒
=
𝟗
𝒙
𝟔
=
𝟑
𝟔
𝟗𝟔
=
𝟒
𝒙
𝟐𝟒
=
𝟏𝟔
𝒙
𝟔
=
𝟒
𝟔
=
𝟐
𝟐𝟒
=
𝟐
𝟒𝒙𝟔
=
𝟒
𝟔
3
PENJUMLAHAN/PENGURANGAN BENTUK AKAR KUADRAT
Ngawi
Jika a Bilangan positif, maka
𝒃 𝒂 + 𝒄 𝒂 = (𝒃 + 𝒄) 𝒂
𝒃 𝒂 − 𝒄 𝒂 = (𝒃 − 𝒄) 𝒂
CONTOH
1).
𝟓𝟎 + 𝟑 𝟑𝟐
2). 3 𝟑𝟎𝟎 − 𝟐 𝟐𝟕
=
𝟐𝟓
𝒙
𝟐
=
𝟓
𝟐
+ 3
𝟏𝟔
𝒙
𝟐
+ 3.
4
𝟐
=
𝟓
𝟐
+ 1
𝟐
𝟐
=
𝟏𝟕
𝟐
=
𝟑
𝟏𝟎𝟎
𝒙
𝟑
=
𝟑
.
𝟏𝟎
𝟑
-
2
𝟗
𝒙
𝟑
-
2.
3
𝟑
=
𝟑𝟎
𝟑
-
6
𝟑
=
𝟐𝟒
𝟑
Jadi
5 𝟐 + 𝟑 𝟐 = 𝟖 𝟐
3 𝟓 +
𝟓 − 𝟐 𝟓 = 𝟐 𝟓
Bagaimana jika dalam bentuk
𝟓𝟎 + 𝟑 𝟑𝟐
???
3). 10 𝟏𝟎𝟎𝟎 + 𝟑 𝟒𝟎𝟎𝟎 -
𝟗𝟎𝟎𝟎
= 10 𝟏𝟎𝟎𝒙𝟏𝟎 + 𝟑 𝟒𝟎𝟎𝒙𝟏𝟎 -𝟗𝟎𝟎𝒙𝟏𝟎
= 10 . 𝟏𝟎 𝟏𝟎 + 𝟑 . 𝟐𝟎 𝟏𝟎 − 𝟑𝟎 𝟏𝟎
= 100 𝟏𝟎 + 𝟔𝟎 𝟏𝟎 − 𝟑𝟎 𝟏𝟎
=
𝟏𝟑𝟎
𝟏𝟎
4
Jika a dan b Bilangan positif,
𝒂 𝒙 𝒃 =
𝒂 𝒙 𝒃
𝒂
𝒃
=
𝒂
𝒃
𝒂 𝒙 𝒂 =
𝒂 𝒙 𝒂 =
𝒂𝟐= 𝒂
PERKALIAN/PEMBAGIAN BENTUK AKAR KUADRAT
Ngawi
CONTOH
𝟏). 𝟔 𝟔 𝒙 𝟑 𝟏𝟐
𝟑). 𝟑 𝟐𝒙𝟒 𝟐𝟒
𝟏𝟖
=
𝟏𝟖
𝟕𝟐
=
𝟏𝟖
𝟑𝟔
𝒙𝟐
=
𝟏𝟖
x
𝟔
𝟐
=
𝟏𝟎𝟖
𝟐
𝟗
𝟑𝒙𝟒 𝟒𝒙𝟔
𝟑
=
4x2
𝟔
=
=
𝟖
𝟔
misal
𝟔 𝒙 𝟑 =
𝟏𝟖
=
𝟑
𝟐
𝟐𝟒
𝟑
=
𝟐
𝟐
2).
𝟒 𝟓𝟒+𝟑 𝟐𝟒
𝟑 𝟐
=
𝟒 𝟗𝒙𝟔+𝟑 𝟒𝒙𝟔
𝟑 𝟐
=
𝟒.𝟑 𝟔+𝟑.𝟐 𝟔
𝟑 𝟐
=
𝟏𝟐 𝟔+𝟔 𝟔
𝟑 𝟐
=
𝟏𝟖 𝟔
𝟑 𝟐
𝟔
𝟑
=
𝟔
𝟑
=
𝟗 𝒙 𝟐
𝟖
=
𝟖
=
𝟒𝒙𝟐
5
Ngawi
MERASIONALKAN PENYEBUT AKAR
𝒎
𝒎
Prasyarat :
𝒂 𝒙 𝒂 =
𝒂𝟐= 𝒂
𝒂 + 𝒃
𝒂 − 𝒃 = 𝒂𝟐− 𝒃𝟐
𝒂
𝒃 = 𝒂
𝒃𝒙 𝒎
𝒎
𝒂 + 𝒃
𝒄 + 𝒅 = 𝒂𝒄 + 𝒂𝒅 + 𝒃𝒄 + 𝒃𝒅
𝒎
𝒎
Contoh :
𝟏
𝟐
𝟒
𝟑 𝟔
𝟓
𝟔 − 𝟐
𝟔 𝟐
𝟓 +
𝟐
Bentuk
𝐚
𝒃
Pembilang dan penyebut dikalikan 𝒃
(nilainya sama)
𝐚
𝒃
=𝐚
𝒃
𝒃
=
𝐚
𝒃𝒙
𝒃
𝒃
Contoh :
𝒎
𝒎
𝟏. 𝟏
𝟐
=
𝟏
𝟐
𝒙
𝟐
𝟐=
𝟐
𝟐
=𝟏
𝟐
𝟐
𝟐.
𝟒
𝟑 𝟔
=
𝟒
𝟑 𝟔
𝒙
𝟔
𝟔
=𝟒 𝟔
𝟑. 𝟔= 𝟒 𝟔
𝟏𝟖
=𝟐
𝟗
𝟔
9
2
𝟑.
𝟐
𝟐 𝟓
=
𝟐
𝟐 𝟓
𝒙
𝟓
𝟓
=
𝟏𝟎
𝟐. 𝟓= 𝟏
𝟏𝟎
𝟏𝟎
6
MERASIONALKAN PENYEBUT AKAR
𝒎
𝒎
Ngawi
Bentuk
𝐚
𝒃 𝒄
Pembilang dan penyebut
Dikalikan dengan SEKAWAN PENYEBUT
Misalkan : Penyebutnya
𝒃 + 𝒄
𝒃 − 𝒄
𝒃 − 𝒄
𝒃 + 𝒄
𝒂 + 𝒃
𝒂 − 𝒃 = 𝒂𝟐− 𝒃𝟐
𝒎
𝒎
Contoh :
𝟓
𝟔 − 𝟐
𝟔 𝟐
𝟓 +
𝟐
1.
2.
=
𝟓
𝟔 − 𝟐𝒙
𝟔 + 𝟐
𝟔 + 𝟐
=𝟓 ( 𝟔 + 𝟐)
𝟔
𝟐 − 𝟐𝟐
=𝟓(√𝟔 +𝟐)
𝟔 − 𝟒
=5√𝟔 + 𝟏𝟎
𝟐
=
𝟔 𝟐
𝟓 +
𝟐
𝒙
𝟓 − √𝟐
𝟓 − √𝟐
=𝟔 𝟐 ( 𝟓 − √𝟐)
𝟓
𝟐 −
𝟐
𝟐
=𝟔 𝟐 ( 𝟓 − √𝟐)
𝟓 − 𝟐
𝟓 + 𝟐
𝟓 − 𝟐
=𝟔 𝟐 ( 𝟓 − √𝟐)
𝟑
2
= 𝟐 𝟐 ( 𝟓 − √𝟐)
= 𝟐 𝟏𝟎 −𝟐. 𝟐
=
𝟓
𝟐 − 𝟐𝟐
= 𝟓
−
𝟒 = 𝟏
= 𝟐 𝟏𝟎 − 𝟒
Ngawi
𝟓𝟒
𝟖
𝟗𝟔
𝟏𝟐 + 𝟐 𝟒𝟖
𝟔 𝟔 𝒙 𝟑 𝟏𝟐
𝟑 𝟐𝒙𝟒 𝟐𝟒
𝟏𝟖
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