Atrisiniet sqrt{frac{sqrt[5]{sqrt{20^{30}*3^{20}*5^60}}}{sqrt[3]{sqrt{sqrt{2^36*3^24*5^48}}}}}

$$\sqrt { \frac { \sqrt[ 5 ] { \sqrt { 20 ^ { 30 } \cdot 3 ^ { 20 } \cdot 5 ^ { 60 } } } } { \sqrt[ 3 ] { \sqrt { \sqrt { 2 ^ { 36 } \cdot 3 ^ { 24 } \cdot 5 ^ { 48 } } } } } }$$

Izrēķināt

$$\frac{25\times 4096^{\frac{23}{24}}\sqrt[20]{9765625}}{1024}\approx 158,113883008$$

Atrisinājuma darbības

Aprēķiniet 20 pakāpē 30 un iegūstiet 1073741824000000000000000000000000000000.

$$\sqrt{\frac{\sqrt[5]{\sqrt{1073741824000000000000000000000000000000\times 3^{20}\times 5^{60}}}}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Aprēķiniet 3 pakāpē 20 un iegūstiet 3486784401.

$$\sqrt{\frac{\sqrt[5]{\sqrt{1073741824000000000000000000000000000000\times 3486784401\times 5^{60}}}}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Reiziniet 1073741824000000000000000000000000000000 un 3486784401, lai iegūtu 3743906242624487424000000000000000000000000000000.

$$\sqrt{\frac{\sqrt[5]{\sqrt{3743906242624487424000000000000000000000000000000\times 5^{60}}}}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Aprēķiniet 5 pakāpē 60 un iegūstiet 867361737988403547205962240695953369140625.

$$\sqrt{\frac{\sqrt[5]{\sqrt{3743906242624487424000000000000000000000000000000\times 867361737988403547205962240695953369140625}}}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Reiziniet 3743906242624487424000000000000000000000000000000 un 867361737988403547205962240695953369140625, lai iegūtu 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{\sqrt[5]{\sqrt{3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000}}}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Aprēķināt kvadrātsakni no 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 un iegūt 1802032470703125000000000000000000000000000000.

$$\sqrt{\frac{\sqrt[5]{1802032470703125000000000000000000000000000000}}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Aprēķināt \sqrt[5]{1802032470703125000000000000000000000000000000} un iegūt 1125000000.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{\sqrt{2^{36}\times 3^{24}\times 5^{48}}}}}}$$

Aprēķiniet 2 pakāpē 36 un iegūstiet 68719476736.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{\sqrt{68719476736\times 3^{24}\times 5^{48}}}}}}$$

Aprēķiniet 3 pakāpē 24 un iegūstiet 282429536481.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{\sqrt{68719476736\times 282429536481\times 5^{48}}}}}}$$

Reiziniet 68719476736 un 282429536481, lai iegūtu 19408409961765342806016.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{\sqrt{19408409961765342806016\times 5^{48}}}}}}$$

Aprēķiniet 5 pakāpē 48 un iegūstiet 3552713678800500929355621337890625.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{\sqrt{19408409961765342806016\times 3552713678800500929355621337890625}}}}}$$

Reiziniet 19408409961765342806016 un 3552713678800500929355621337890625, lai iegūtu 68952523554931640625000000000000000000000000000000000000.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{\sqrt{68952523554931640625000000000000000000000000000000000000}}}}}$$

Aprēķināt kvadrātsakni no 68952523554931640625000000000000000000000000000000000000 un iegūt 8303765625000000000000000000.

$$\sqrt{\frac{1125000000}{\sqrt[3]{\sqrt{8303765625000000000000000000}}}}$$

Aprēķināt kvadrātsakni no 8303765625000000000000000000 un iegūt 91125000000000.

$$\sqrt{\frac{1125000000}{\sqrt[3]{91125000000000}}}$$

Aprēķināt \sqrt[3]{91125000000000} un iegūt 45000.

$$\sqrt{\frac{1125000000}{45000}}$$

Daliet 1125000000 ar 45000, lai iegūtu 25000.

$$\sqrt{25000}$$

Sadaliet reizinātājos 25000=50^{2}\times 10. Pārrakstiet reizinājuma kvadrātsakni \sqrt{50^{2}\times 10} kā kvadrātveida saknes \sqrt{50^{2}}\sqrt{10}. Izvelciet kvadrātsakni no 50^{2}.

$$50\sqrt{10}$$