Question

Pilne na jutro!!!
1.Doprowadż do najprostszej postaci wyrażenia:

a) √8-√32+√128
b) √27+√48-√75
c) √125+√24-√45-√150
d) √175+√80-√28-√180
e) (√3+2√2)(3√2-4√3)
f) (√7-5√3)(2√7+√3)

Answer 1

A)√8-√32+√128=2√2-4√2+8√2=6√2
b)√27+√48-√75=3√3+4√3-5√3=2√3
c)√125+√24-√45-√150 to jest najprostsza postac
d)√175+√80-√28-√180 to jest najprostsza postac
e)(√3+2√2)(3√2-4√3)=

Answer 2

A)
√8-√32+√128=
=√4*√2-√16*√2+√64*√2=
= 2*√2 - 4*√2 +8*√2 =
= 6√2

b)
√27+√48-√75=
=√9*√3 + √16*√3 - √25*√3=
= 3*√3 + 4*√3 - 5*√3=
= 2√3

c)
√125+√24-√45-√150=
= √25*√5 + √4*√6 - √9*√5 - √25*√6=
= 5*√5 + 2*√6 - 3*√5 - 5*√6=
= 2√5 - 3√6

d)
√175+√80-√28-√180
=√25*√7 + √16*√5 - √4*√7 - √36*√5=
= 5*√7 + 4*√5 - 2*√7 - 6*√5 =
= 3√7 - 2√5
e)
(√3+2√2)(3√2-4√3)=
= 3*√3*√2 - 4√3* √3 + 6*√2*√2 - 8*√2*√3 =
= 3*√6 - 4*3 + 6*2 - 8*√6=
= - 5√6 -12 + 12 =
= -5√6

f)
(√7-5√3)(2√7+√3) =
= 2*√7*√7 + √7*√3 - 10*√3*√7 - 5*√3*√3=
= 2*7 + √21 - 10√21 - 5*3=
= 14 - 9√21 - 15=
= -1 -9√21