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

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

Aromātai

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

Ngā Upane Otinga

Tātaihia te 20 mā te pū o 30, kia riro ko 1073741824000000000000000000000000000000.

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

Tātaihia te 3 mā te pū o 20, kia riro ko 3486784401.

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

Whakareatia te 1073741824000000000000000000000000000000 ki te 3486784401, ka 3743906242624487424000000000000000000000000000000.

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

Tātaihia te 5 mā te pū o 60, kia riro ko 867361737988403547205962240695953369140625.

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

Whakareatia te 3743906242624487424000000000000000000000000000000 ki te 867361737988403547205962240695953369140625, ka 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000.

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

Tātaitia te pūtakerua o 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 kia tae ki 1802032470703125000000000000000000000000000000.

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

Tātaitia te \sqrt[5]{1802032470703125000000000000000000000000000000} kia tae ki 1125000000.

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

Tātaihia te 2 mā te pū o 36, kia riro ko 68719476736.

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

Tātaihia te 3 mā te pū o 24, kia riro ko 282429536481.

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

Whakareatia te 68719476736 ki te 282429536481, ka 19408409961765342806016.

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

Tātaihia te 5 mā te pū o 48, kia riro ko 3552713678800500929355621337890625.

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

Whakareatia te 19408409961765342806016 ki te 3552713678800500929355621337890625, ka 68952523554931640625000000000000000000000000000000000000.

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

Tātaitia te pūtakerua o 68952523554931640625000000000000000000000000000000000000 kia tae ki 8303765625000000000000000000.

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

Tātaitia te pūtakerua o 8303765625000000000000000000 kia tae ki 91125000000000.

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

Tātaitia te \sqrt[3]{91125000000000} kia tae ki 45000.

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

Whakawehea te 1125000000 ki te 45000, kia riro ko 25000.

$$\sqrt{25000}$$

Tauwehea te 25000=50^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{50^{2}\times 10} hei hua o ngā pūtake rua \sqrt{50^{2}}\sqrt{10}. Tuhia te pūtakerua o te 50^{2}.

$$50\sqrt{10}$$