Zad.1
Oblicz.
a) (7√2 - 3√8) x √2 =
b) (2√8 + 3√18 + √50 - 2√72) x √2 =
c) (4√12 - 8√27 + √48 - 2√75) x √3 =
d) (7√2 - 3√8 + 3√18) x √2 =
Zad.2
Oblicz.
a) √20 + 2√45 - 3√80 =
b) 2√2 - 3√8 + 5√18 =
c) 2∛3 - 4∛24 +3∛81 =
d) √12 - 3√3 + √48
------------------- =
√3
e) ∛2 - 2∛16 + ∛54
--------------------- =
4∛2
f) ∛4 + 2∛32 - ∛108
---------------------- =
3∛32
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Zad.1
a) (7√2 - 3√8) x √2 = (7√2 - 3√4*2) * √2 = (7√2 - 6√2)* √2 =√2 *√2 = 2
b) (2√8 + 3√18 + √50 - 2√72) x √2 = (2√4*2 + 3√9*2 +√25*2 - 2√36*2) * √2 = (4√2 + 9√2 + 5√2 - 12√2) * √2 = 6√2 * √2 = 6 * 2 =12
c) (4√12 - 8√27 + √48 - 2√75) x √3 = (4√4*3 - 8√9*3 +√16*3 - 2√25*3) * √3 = (8√3 - 24√3 + 4√3 - 10√3) * √3 = -22√3 * √3 = -22 * 3 = -66
d) (7√2 - 3√8 + 3√18) x √2 = (7√2 - 3√4*2 + 3√9*2) *√2 = (7√2 - 6√2 + 9√2) *√2 = 10√2 *√2 = 10 * 2 =20
Zad.2
a) √20 + 2√45 - 3√80 =√4*5 + 2√9*5 - 3√16*5 = 2√5 + 6√5 - 12√5 = -5√5
b) 2√2 - 3√8 + 5√18 = 2√2 - 3√4*2 + 5√9*2 = 2√2 - 6√2 + 15√2 = 11√2
c) 2∛3 - 4∛24 +3∛81 = 2∛3 - 4∛8*3 + 3∛27*3 = 2∛3 - 8∛3 + 9∛3 = 3∛3
d) √12 - 3√3 + √48 √4*3 - 3√3 +√16*3 2√3 - 3√3 + 4√3 3√3
------------------- = ------------------- = ------------------ = -------- = 3
√3 √3 √3 √3
e) ∛2 - 2∛16 + ∛54 ∛2 - 2∛8*2 +∛27*2 ∛2 - 4∛2 +3∛2 ∛2
--------------------- = ----------------------- = ------------------ = ------ = 1/4
4∛2 4∛2 4∛2 4∛2
f) ∛4 + 2∛32 - ∛108 ∛4 + 2∛8*4 -∛27*4 ∛4 + 4∛4 - 3∛4 2∛4
---------------------- = ----------------------- = ----------------- = ------------ = 2/6 = 1/3
3∛32 3∛8*4 6∛4 6∛4
a) (7√2 - 3√8) x √2 =
(7√2-√72)·√2
(7√2-6√2)·√2
√2·√2=2
b) (2√8 + 3√18 + √50 - 2√72) x √2 =
(√32+√162+√50-√288)·√2=
(4√2+9√2+5√2-12√2)·√2=
6√2·√2=12
c) (4√12 - 8√27 + √48 - 2√75) x √3 =
(8√3-16√3+4√3-10√3)·√3
-14√3·√3=-42
d) (7√2 - 3√8 + 3√18) x √2 =
(7√2-√72+√162)·√2=
(7√2-6√2+9√2)·√2=
10√2·√2=20
Zad.2
Oblicz.
a) √20 + 2√45 - 3√80 =
√4·5 +2√5·9 - 3√5·16
2√5+6√5-12√5=
-4√5
b) 2√2 - 3√8 + 5√18 =
2√2-3√2·4 +5√2·9
2√2-6√2+15√2=11√2
c) 2∛3 - 4∛24 +3∛81 =
2∛3-4∛8·3+3∛27·3
2∛3-8∛3+9∛3=3∛3
d) √12 - 3√3 + √48
2√3-3√3+√16·3
2√3-3√3+4√3=3√3
e) ∛2 - 2∛16 + ∛54=
∛2-2∛8·2+∛27·2
∛2-4∛2+3∛2=0
f) ∛4 + 2∛32 - ∛108=
∛4+2∛8·4-∛27·4
∛4+4∛4-3∛4=2∛4