Question

ZAD 1. Oblicz:

a) 2

b)

c)

ZAD 2. Usuń niewymierność z mianownika:

a) 2

b) 3

Answer 1

Zad.1

a)

2√625 - 4√144 + 3∛729 = 2·25 - 4·12 + 3·9 = 50-48+27 = 29

 

b)

   2√768-5√720 - 4√1200 + 3√1620 =

= 2·√(256·3) - 5√(144·5) - 4√(400·3) + 3√(324·5) =

= 2·√256·√3 - 5·√144·√5 - 4·√400·√3 + 3√324·√5 =

= 2·16·√3 - 5·12·√5 - 4·20·√3 + 3·18·√5 =

= 32√3 - 60√5 - 80√3 + 54√5 =

= -6√5 - 48√3 =

= -6(√5+8√3)

 

c)

   (2⁴ : 16⁻⁵ · 8²)⁻¹ =

= ((2⁴ : (2⁴)⁻⁵ · (2³)²))⁻¹ =

= (2⁴ : 2⁻²⁰ · 2⁶)⁻¹ =

= (2⁴⁺²⁰⁺⁶)⁻¹ =

= (2³⁰)⁻¹ =

= 2⁻³⁰ =

= (1/2)³⁰

 

Zad.2

a)

  (2+3√3)/2√6 · √6/√6 = √6(2+3√3)/(2·6) = ((2√6+3√18)/12 = ((2√6+3√(9·2))/12 = =(2√6+3√9·√2)/12 = (2√6+3·3√2)/12 = (2√6+9√2)/12

 

b)

3∛6/∛2 = 3∛(6/2) = 3∛3