9D7Uf

Apskaičiuokite $\sqrt[6]{14-6\cdot \sqrt {5}}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$

Sprendimas.

saknis(6,

14- 6* saknis(

5))* saknis(3,

(3+saknis(

5)))* saknis(3,

2) =

saknis(6,

14- 6* saknis(

5))* saknis(3,

(3+saknis(

5)))* saknis(3,

2) = $\sqrt[6]{14-6\cdot \sqrt {5}}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

saknis(6,

9+5- 6* saknis(

5))* saknis(3,

(3+saknis(

5)))* saknis(3,

2) = $\sqrt[6]{9+5-6\cdot \sqrt {5}}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

saknis(6,

9- 6* saknis(

5)+5)* saknis(3,

(3+saknis(

5)))* saknis(3,

2) = $\sqrt[6]{9-6\cdot \sqrt {5}+5}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

saknis(6,

3^²- 6* saknis(

5)+5)* saknis(3,

(3+saknis(

5)))* saknis(3,

2) = $\sqrt[6]{3^{2}-6\cdot \sqrt {5}+5}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

saknis(6,

3^²- 2* 3* saknis(

5)+5)* saknis(3,

(3+saknis(

5)))* saknis(3,

2) = $\sqrt[6]{3^{2}-2\cdot 3\cdot \sqrt {5}+5}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[6]{14-6\cdot \sqrt {5}}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[6]{9-6\cdot \sqrt {5}+5}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[6]{3^{2}-2\cdot 3\cdot \sqrt {5}+5}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[6]{(3-\sqrt {5})^{2}}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[3]{3-\sqrt {5}}\cdot \sqrt[3]{(3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[3]{(3-\sqrt {5})\cdot (3+\sqrt {5})}\cdot \sqrt[3]{2}$ =

$\sqrt[3]{(3^{2}-\sqrt {5}^{2})}\cdot \sqrt[3]{2}$ =

$\sqrt[3]{(3^{2}-5)}\cdot \sqrt[3]{2}$ =

$\sqrt[3]{4}\cdot \sqrt[3]{2}$ =

$\sqrt[3]{8}$ =

$2$

Atsakymas: 2