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Matematika Házi
Chimmy_Rika 13
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Csatoltam képet
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Középiskola / Matematika
Válaszok
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Nagy-Gombás Szilvi
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válasza
6. feladat:
a) 8/√ 2 = (8/√ 2 ) * (√ 2 /√ 2 ) = (8√ 2 ) / (√ 2 )2 = (8√ 2 / 2 = 4√ 2
b) 9/3√ 3 = 3/√ 3 = (3/√ 3 ) * (√ 3 /√ 3 ) = (3√ 3 ) / (√ 3 )2 = (3√ 3 / 3 = √ 3
c) -12/√ 18 = (-12/√ 18 ) * (√ 18 /√ 18 ) = (-12√ 18 ) / (√ 18 )2 = (-12√ 18 / 18 = -2√ 18 / 3 = -2√ 9 *2 / 3 = -2 * 3√ 2 / 3 = -6√ 2 / 3 = -2√ 2
d) -30/2√ 5 = -15/√ 5 = (-15/√ 5 ) * (√ 5 /√ 5 ) = (-15√ 5 ) / (√ 5 )2 = (-15√ 5 / 5 = -3√ 5
e) 6/√ 3 = (6/√ 3 ) * (√ 3 /√ 3 ) = (6√ 3 ) / (√ 3 )2 = (6√ 3 / 3 = 2√ 3
f) 4/2√ 2 = 2/√ 2 = (2/√ 2 ) * (√ 2 /√ 2 ) = (2√ 2 ) / (√ 2 )2 = (2√ 2 / 2 = √ 2
g) -10√ 5 /3√ 10 = (-10√ 5 /3√ 10 ) * (√ 10 /√ 10 ) = (-10√ 5 * √ 10 ) / 3(√ 10 )2 = (-10√ 50 / (3 * 10) = (-10√ 50 ) / 30 = -√ 50 / 3 = - √ 25 * 2 / 3 = -5√ 2 / 3
h) 2√ 3 /√ 8 = (2√ 3 /√ 8 ) * (√ 8 /√ 8 ) = (2√ 3 * √ 8 ) / (√ 8 )2 = (2√ 24 / 8 = (√ 24 ) / 4 = √ 4 * 6 / 4 = 2√ 6 / 4 = √ 6 / 2
i) 3√ 5 /√ 12 = (3√ 5 /√ 12 ) * (√ 12 /√ 12 ) = (3√ 5 * √ 12 ) / (√ 12 )2 = (3√ 60 / 12 = (√ 60 ) / 4 = √ 4 * 15 / 4 = 2√ 15 / 4 = √ 15 / 2
j) -8√ 5 /√ 32 = (-8√ 5 /√ 32 ) * (√ 32 /√ 32 ) = (-8√ 5 * √ 32 ) / (√ 32 )2 = (-8√ 160 / 32 = -(√ 160 ) / 4 = -√ 16 * 10 / 4 = -4√ 10 / 4 = -√ 10
k) 3/√ 18 = (3/√ 18 ) * (√ 18 /√ 18 ) = (3√ 18 ) / (√ 18 )2 = (3√ 18 / 18 = √ 18 / 6 = √ 9 * 2 / 6 = 3√ 2 / 6 = √ 2 / 2
l) -4/√ 12 = (-4/√ 12 ) * (√ 12 /√ 12 ) = (-4√ 12 ) / (√ 12 )2 = (-4√ 12 / 12 = -√ 12 / 3 = -√ 4 * 3 / 3 = -2√ 3 / 3
a) 8/√ 2 = (8/√ 2 ) * (√ 2 /√ 2 ) = (8√ 2 ) / (√ 2 )2 = (8√ 2 / 2 = 4√ 2
b) 9/3√ 3 = 3/√ 3 = (3/√ 3 ) * (√ 3 /√ 3 ) = (3√ 3 ) / (√ 3 )2 = (3√ 3 / 3 = √ 3
c) -12/√ 18 = (-12/√ 18 ) * (√ 18 /√ 18 ) = (-12√ 18 ) / (√ 18 )2 = (-12√ 18 / 18 = -2√ 18 / 3 = -2√ 9 *2 / 3 = -2 * 3√ 2 / 3 = -6√ 2 / 3 = -2√ 2
d) -30/2√ 5 = -15/√ 5 = (-15/√ 5 ) * (√ 5 /√ 5 ) = (-15√ 5 ) / (√ 5 )2 = (-15√ 5 / 5 = -3√ 5
e) 6/√ 3 = (6/√ 3 ) * (√ 3 /√ 3 ) = (6√ 3 ) / (√ 3 )2 = (6√ 3 / 3 = 2√ 3
f) 4/2√ 2 = 2/√ 2 = (2/√ 2 ) * (√ 2 /√ 2 ) = (2√ 2 ) / (√ 2 )2 = (2√ 2 / 2 = √ 2
g) -10√ 5 /3√ 10 = (-10√ 5 /3√ 10 ) * (√ 10 /√ 10 ) = (-10√ 5 * √ 10 ) / 3(√ 10 )2 = (-10√ 50 / (3 * 10) = (-10√ 50 ) / 30 = -√ 50 / 3 = - √ 25 * 2 / 3 = -5√ 2 / 3
h) 2√ 3 /√ 8 = (2√ 3 /√ 8 ) * (√ 8 /√ 8 ) = (2√ 3 * √ 8 ) / (√ 8 )2 = (2√ 24 / 8 = (√ 24 ) / 4 = √ 4 * 6 / 4 = 2√ 6 / 4 = √ 6 / 2
i) 3√ 5 /√ 12 = (3√ 5 /√ 12 ) * (√ 12 /√ 12 ) = (3√ 5 * √ 12 ) / (√ 12 )2 = (3√ 60 / 12 = (√ 60 ) / 4 = √ 4 * 15 / 4 = 2√ 15 / 4 = √ 15 / 2
j) -8√ 5 /√ 32 = (-8√ 5 /√ 32 ) * (√ 32 /√ 32 ) = (-8√ 5 * √ 32 ) / (√ 32 )2 = (-8√ 160 / 32 = -(√ 160 ) / 4 = -√ 16 * 10 / 4 = -4√ 10 / 4 = -√ 10
k) 3/√ 18 = (3/√ 18 ) * (√ 18 /√ 18 ) = (3√ 18 ) / (√ 18 )2 = (3√ 18 / 18 = √ 18 / 6 = √ 9 * 2 / 6 = 3√ 2 / 6 = √ 2 / 2
l) -4/√ 12 = (-4/√ 12 ) * (√ 12 /√ 12 ) = (-4√ 12 ) / (√ 12 )2 = (-4√ 12 / 12 = -√ 12 / 3 = -√ 4 * 3 / 3 = -2√ 3 / 3
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