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

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

Luacháil

$$\frac{25\times 4096^{\frac{23}{24}}\sqrt[20]{9765625}}{1024}\approx 158.113883008$$

Céimeanna Réitigh

Ríomh cumhacht 20 de 30 agus faigh 1073741824000000000000000000000000000000.

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

Ríomh cumhacht 3 de 20 agus faigh 3486784401.

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

Méadaigh 1073741824000000000000000000000000000000 agus 3486784401 chun 3743906242624487424000000000000000000000000000000 a fháil.

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

Ríomh cumhacht 5 de 60 agus faigh 867361737988403547205962240695953369140625.

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

Méadaigh 3743906242624487424000000000000000000000000000000 agus 867361737988403547205962240695953369140625 chun 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 a fháil.

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

Áirigh fréamh chearnach 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 agus faigh 1802032470703125000000000000000000000000000000.

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

Áirigh \sqrt[5]{1802032470703125000000000000000000000000000000} agus faigh 1125000000.

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

Ríomh cumhacht 2 de 36 agus faigh 68719476736.

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

Ríomh cumhacht 3 de 24 agus faigh 282429536481.

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

Méadaigh 68719476736 agus 282429536481 chun 19408409961765342806016 a fháil.

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

Ríomh cumhacht 5 de 48 agus faigh 3552713678800500929355621337890625.

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

Méadaigh 19408409961765342806016 agus 3552713678800500929355621337890625 chun 68952523554931640625000000000000000000000000000000000000 a fháil.

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

Áirigh fréamh chearnach 68952523554931640625000000000000000000000000000000000000 agus faigh 8303765625000000000000000000.

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

Áirigh fréamh chearnach 8303765625000000000000000000 agus faigh 91125000000000.

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

Áirigh \sqrt[3]{91125000000000} agus faigh 45000.

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

Roinn 1125000000 faoi 45000 chun 25000 a fháil.

$$\sqrt{25000}$$

Fachtóirigh 25000=50^{2}\times 10. Athscríobh fréamh cearnach an toraidh \sqrt{50^{2}\times 10} mar thoradh na bhfréamhacha cearnacha \sqrt{50^{2}}\sqrt{10}. Tóg fréamh chearnach 50^{2}.

$$50\sqrt{10}$$