Question

Wyłacz czynnik przed pierwiastek:
a) √32, √75, √40
b) √200, √108, √810
c)√¾, √²/₂₅, √⁵/₄₉
d)∛40, ∛96, ∛242
e)√12*24
f)√22*11
g)√30*10*15
h)∛24*18*12 *=razy

Answer 1

A)
√32 = √16 * 2 = √16 * √2 = 4√2
√75 = √25 * 3 = √25 * √3 = 5√3
√40 = √4 * 10 = √4 * √10 = 2√10

b)
√200 = √100 * 2 = √100 * √2 = 10√2
√108 = √36 * 3 = √36 * √3 = 6√3
√810 = √81 * 10 = √81 * √10 = 9√10

c)√¾ = √3 : √4 = √3 : 2 = 1/2 √3
√²/₂₅ = √2 : √25 = √2 : 5 = 1/5 √2
√⁵/₄₉ = √5 : √49 = √5 : 7 = 1/7√5

d)
∛40 = ∛8 * ∛5 = 2∛5
∛96 = ∛8 * ∛12 = 2∛12
√242 = √2 * √121 = 11√2

e)√12*24 = √3 * 4 * 3 * 8 = √9 * 32 = √9 * √32 = 3 * √16 * √2 = 3 * 4√2 = 12√2

f)√22*11 = √11 * 2 * 11 = √121 * √2 = 11√2

g)√30*10*15 = √3 * 10 * 10 * 3 * 5 = √9 * √100 * √5 = 3 * 10 * √5 = 30√5

h)∛24*18*12 * = ∛8 * 3 * 9 * 2 * 4 * 3 = ∛27 * ∛8 * ∛8 * ∛3 = 3 * 2 * 2 * ∛3 = 12∛3

Answer 2

A] 4 \/2
5 \/3 ,2 \/10
b]10 \/2
6 \/3
9 \/10
c]-
d]4*10=40
6*4=12
22*11
e]6 \/8
f]11 \/2
g]5 \/180
h]72

Answer 3

A)√4*8=4√2 ,√75=√3*25=5√3 ,√40=√4*10=2√10
b)√200 =√2*100=10√2,√108=√4*27=2√3*9=6√3 , √810=√81*10=9√10
c)√3/4=√3/2 ,√1/4=1/2
d)√40=2√10,√96=4√6, √242=√2*121=11√2
e)√12*24=√12*2*12=12√2
f)√22*11=√2*11*11=11√2
g)√30*10*15=√2*15*10*15=15√20=30√5
h)√24*18*12=√2*12*18*12=12√36=36√4=72