Question

1.przedstaw liczbe w postaci a√b

a.) 2√18+√50

b.)√12-2√75

c.)2√20-7√45

d.)√242+0,25√32-1/3√72

2.oblicz

a.)√144/121

b.)√324/289

c.)√225/361

d.)√169/196

e.)√2 1/144

f.)√1 48/121

Answer 1

1.przedstaw liczbe w postaci a√b

a.) 2√18+√50=

= 2√(9*2) + √(25*2) =

= 2*√9*√2 + √25*√2 =

= 2*3√2 + 5√2 =

= 6√2 +5√2 =

= 11√2

 

b.)√12-2√75=

= √(4*3) - 2*√(25*3) =

= √4*√3 - 2*√25*√3 =

= 2√3 -2*5*√3 =

= 2√3 -10√3 =

= -8√3

 

c.)2√20-7√45 =

= 2*√(4*5) -7*√(9*5) =

= 2*√4*√5 - 7*√9*√5 =

= 2*2*√5 - 7*3*√5 =

= 4√5 - 21√5 =

= - 17√5

 

d.)√242+0,25√32-1/3√72 =

= √(121*2) +¼*√(16*2) - ⅓*√(36*2) =

= √121*√2 + ¼*√16*√2 - ⅓*√36*√2 =

= 11*√2 + ¼*4*√2 - ⅓*6*√2 =

 = 11√2 + √2 - 2√2 =

= 10√2

 

2.oblicz

a.)√144/121=

= √144 : √121 =

= 12 : 11 =

= 12/11=

= 1 i 1/11

 

 

b.)√324/289=

= √324 : √289=

= 18 : 17 =

= 18/17 =

= 1 i 1/17

 

c.)√225/361=

= √225 : √361 =

= 15 : 19 =

= 15/19

 

d.)√169/196=

= √169 : √196 =

= 13 : 14 =

= 13/14

 

e.)√2 1/144=

= √289/144 =

= √289 : √144 =

= 17 : 12 =

= 17/12 =

= 1 i 5/12

 

f.)√1 48/121=

= √169/121 =

= √169 : √121=

= 13 : 11 =

= 13/11 =

= 1 i 2/11

Answer 2

1. a) 2√18+√50 = 2*3√2+5√2 = 6√2+5√2 = 11√2 b) √12-2√75 = 2√3-2*5√3 = 2√3-10√3 = -8√3 c) 2√20-7√45 = 2*2√5-7*3√5 = 4√5-21√5 = -17√5 d √242+0,25√32-1/3√72 = 11√2+1/4*4√2-1/3*6√2 = 11√2+√2-2√2 = 10√2 2. a)√144/√121 = 12/11 b)√324/√289 = 18/17 c)√225/√361 = 15/19 d)√169/√196 = 13/14 e)√21/√144 = √21/12 f)√148/√121 = 2√37/11