Page 38 - math 12

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ٍﺔﻴﻌﻴﺑﺮﺗ ﺭﻭﺬﺟ ﻰﻠﻋ ﻱﻮﺘﺤﺗ ﻲﺘﻟﺍ ﺔﻳﺩﺪﻌﻟﺍ ﻞﻤُﺠﻟﺍ ﻂﻴﺴﺒﺗ ُ ﺱﺭﺪﻟﺍ
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َ
Simplifying the Numerical Sentences which contain Square Roots [2-3]

ﻢﻠﻌﺗ ﺱﺭﺪﻟﺍ ُﺓﺮﻜﻓ
ِ
ﻲﻫﻭ
ﻲﺘﻟﺍ ﻲﻫﻭ ﺐﻜﻨﻌﻟﺍ ﻰﺜﻧﺍ ﻲﻫ ُﺕﻮﺒﻜﻨﻌﻟﺍ ﻞﻤـَﺠﻟﺍ ﻂﻴﺴﺒﺗ
ﻲﺘﻟﺍ
ﻲﻫ ُ

ﻰﺜﻧﺍ
ﺕﻮﺒﻜﻨﻌﻟﺍ
ﺐﻜﻨﻌﻟﺍ
ُ
َ
ﻁﻮﻴﺨﻟﺍ ُﺩﺪﻋ ﻞﺼﺗﻭ ﺕﻮﺒﻜﻨﻌﻟﺍ ﺖﻴﺑ ﻲﻨﺒﺗ
ﻁﻮﻴﺨﻟﺍ ُﺩﺪﻋ ﻞﺼﺗﻭ ﺕﻮﺒﻜﻨﻌﻟﺍ ﺖﻴﺑ ﻲﻨﺒﺗ ﻱﻮﺘﺤﺗ ﻲﺘﻟﺍ ﺔﻳﺩﺪﻌﻟﺍ
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ﺪﺣﺍﻮﻟﺍ ﻂﻴﺨﻟﺍ ﻝﻮﻁﻭ ﻂﻴﺧ ﻒﻟﺍ 400 ﻰﻟﺍ
ﺪﺣﺍﻮﻟﺍ ﻂﻴﺨﻟﺍ ﻝﻮﻁﻭ ﻂﻴﺧ ﻒﻟﺍ
ٌٌ
ٌٌ
ﺖﻴﺒﻟ ﺔﻴﻨﻓ ﺔﺣﻮﻟ ﻡﺎﺴﺑ ﻢﺳﺭ ، .ﺔﻴﻌﻴﺑﺮﺗ ﺭﻭﺬﺟ ﻰﻠﻋ
ﺖﻴﺒﻟ ﺔﻴﻨﻓ ﺔﺣﻮﻟ ﻡﺎﺴﺑ ﻢﺳﺭ ، 20cm
ُُ
ََ
ﻞﻴﻄﺘﺴﻣ ﻲﺟﺎﺟﺯ ﺡﻮﻟ ﻰﻠﻋ ﺕﻮﺒﻜﻨﻌﻟﺍ ﺕﺍﺩﺮﻔﻤﻟﺍ
ﻞﻴﻄﺘﺴﻣ ﻲﺟﺎﺟﺯ ﺡﻮﻟ ﻰﻠﻋ ﺕﻮﺒﻜﻨﻌﻟﺍ
ّّ
ٍٍ
3 3 2 cm ﻪﺿﺮﻋﻭ 5 18 cm ﻪﻟﻮﻁ .ﻡﺎﻘﻤﻟﺍ ﺐﻴﺴﻨﺗ
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؟ ِﺔﻴﻨﻔﻟﺍ ِﺔﺣﻮﻠﻟﺍ ﻂﻴﺤﻣ ﺎﻣ
(ﻊﻳﺯﻮﺘﻟﺍ ﻭ ﻊﻴﻤﺠﺘﻟﺍﻭ ﻝﺍﺪﺑﻷﺍ ) ﺹﺍﻮﺨﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻳﺩﺪﻌﻟﺍ ﻞﻤﺠﻟﺍ ﻂﻴﺴﺒﺗ [
(ﻊﻳﺯﻮﺘﻟﺍ ﻭ ﻊﻴﻤﺠﺘﻟﺍﻭ ﻝﺍﺪﺑﻷﺍ ) ﺹﺍﻮﺨﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻳﺩﺪﻌﻟﺍ ﻞﻤﺠﻟﺍ ﻂﻴﺴﺒﺗ [2-3-1]
Simplifying the Numerical Sentences by using the properties (Commutative , accusative, distributive)
ﺏﻮﻠﺳﻷﺎﺑﻭ ،ﺩﺍﺪﻋﻷﺍ ﺹﺍﻮﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﺒﺴﻧ ٍﺩﺍﺪﻋﺍ ﻰﻠﻋ ﻱﻮﺘﺤﺗ ﻲﺘﻟﺍ ﺔﻳﺩﺪﻌﻟﺍ ﻞﻤﺠﻟﺍ ﻂﻴﺴﺒﺗ ﺎﻘﺑﺎﺳ َﺖﻤﻠﻌﺗ
ﻝﺍﺪﺑﻷﺍ) ﺹﺍﻮﺨﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ٍﺔﻴﻌﻴﺑﺮﺗ ﺭﻭﺬﺟ ﻰﻠﻋ ﻱﻮﺘﺤﺗ ﻲﺘﻟﺍ ﺔﻳﺩﺪﻌﻟﺍ ﻞﻤﺠﻟﺍ ﻂﻴﺴﺒﺗ ﻢﻠﻌﺘﺗ ﻑﻮﺳ ﻪﺴﻔﻧ
ِ
ٍ
:ﺔﻴﺗﻵﺍ ﺹﺍﻮﺨﻟﺍ ﻝﺎﻤﻌﺘﺳﺍ ﻦﻜﻤﻳﻭ ( ﻊﻳﺯﻮﺘﻟﺍﻭ ﻊﻴﻤﺠﺘﻟﺍﻭ
ِ
ِ
i) ab = a b , ∀ a,b ≥ 0
a a
=
ii) a a = a , ∀ a ≥ 0 iii) ∀ a ≥ 0 , b > 0
,
b b
َ
ﻲﺘﻟﺍ 5 18 cm ، 3 2 cm ﺎﻫُﺩﺎﻌﺑﺃ ﻲﺘﻟﺍ ﻞﻜﺸﻟﺍ ِﺔﻠﻴﻄﺘﺴﻤﻟﺍ ِﺔﻴﻨﻔﻟﺍ ِﺔﺣﻮﻠﻟﺍ ﻂﻴﺤﻣ ْﺪﺟ (1) ﻝﺎﺜﻣ
ِ
ِ
. ﻡﺎﺴﺑ ﺎﻬﻤﺳﺭ
P = 2 ( L+ W ) W ﺽﺮﻌﻟﺍ ، L ﻝﻮﻄﻟﺍ ، P ﻂﻴﺤﻤﻟﺍ : ﻞﺜﻤﺗ ﺕﺍﺮﻴﻐﺘﻤﻟﺍ
ْ
ِ
= 2 ( 5 18 + 3 2 ) ﻊﻳﺯﻮﺘﻟﺍ ﺔﻴﺻﺎﺧ ﻞﻤﻌﺘﺳﺍ
= 2 × 5 18 + 2 × 3 2
= 10 × 9 2 + 6 2 9 2 ﻮﻫ ﺎﻬﻳﻭﺎﺴﻳ ﺎﻤﺑ 18 ﻦﻋ ﺽﻮﻋ
= 10 × 3 2 + 6 2 3 ﻮﻫ ﺎﻬﻳﻭﺎﺴﻳ ﺎﻤﺑ 9 ﻦﻋ ﺽﻮﻋ
ﺔﻬﺑﺎﺸﺘﻤﻟﺍ ﺩﻭﺪﺤﻟﺍ ﻊﻤﺠﺑ ﺭﺍﺪﻘﻤﻟﺍ ﻂﻴﺴﺒﺗ
= 30 2 + 6 2

= 36 2 36 2 cm ﻮﻫ ﺔﻴﻨﻔﻟﺍ ﺔﺣﻮﻠﻟﺍ ﻂﻴﺤﻣ ﻝﻮﻁ ﻥﺫﺇ

: (ﻊﻳﺯﻮﺘﻟﺍﻭ ﻊﻴﻤﺠﺘﻟﺍﻭ ﻝﺍﺪﺑﻷﺍ) ﺹﺍﻮﺨﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﻟﺎﺘﻟﺍ ﺔﻳﺩﺪﻌﻟﺍ ﻞﻤﺠﻟﺍ ِﻂّﺴَﺑ (2) ﻝﺎﺜﻣ
ِ
ِ
ِ

i) 5 12 -7 32 = 5 3 × 4 - 7 ii) 5 ( 10 + 3 ) = 5 10 + 5 3
2 × 16
= 5 3 4 - 7 2 16 = 50 + 15
= 5 4 3 - 7 16 2 = + 15

25 × 2
= (5×2) 3 - (7×4) 2 = 25 2 + 15

= 10 3 - 28 2 = 5 2 + 15

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