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Wyłącz czynnik przed znak pierwiastka
a) √108 = √9*√3*√4 = 3*2*√3 = 6√3
b) √3⅕ = √(16/5) = √16 : √5 = 4:√5 = 4√5:5= (4/5)√5
c) ³√5,4 = ∛(54/10) = ∛ 27:∛5= 3 / ∛5 = 3*∛25/5 = (3/5)∛25
Zad.6
Wyłącz czynnik pod znak pierwiastka
a) 3√5 = √ (9*5) = √45
b) ⅖√15 = √(4/25*15) = √(12/5)= √24/10 = √2,4
c) 2 ³√¼ = ∛(8*1/4) = ∛2
d) 0,3 ³√100 = (3/10) ∛100= ∛ (27*100:1000 = ∛2,7
Zad.7
Zapisz w prostszej postaci.
a) ½√72-¼√32+⅕√50 =
= 1/2*√36*√2 - 1/4*√16*√2 + 1/5*√25*√2=
= 1/2*6*√2 - 1/4*4*√2 + 1/5*5*√2=
= 3√2 - √2 +√2 =
= 3√2
b) 0,2³√250-0,25³√128+⅓³√54 =
= 1/5*∛125*∛2 - 1/4*∛ 64*∛2 + 1/3*∛27*∛2=
= 1/5*5*∛2 - 1/4*4*∛2 + 1/3*3*∛2=
= ∛2 - ∛2 + ∛2 =
= ∛2