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

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

វាយតម្លៃ

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

ជំហានចម្លើយ

គណនាស្វ័យគុណ 20 នៃ 30 ហើយបាន 1073741824000000000000000000000000000000។

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

គណនាស្វ័យគុណ 3 នៃ 20 ហើយបាន 3486784401។

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

គុណ 1073741824000000000000000000000000000000 និង 3486784401 ដើម្បីបាន 3743906242624487424000000000000000000000000000000។

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

គណនាស្វ័យគុណ 5 នៃ 60 ហើយបាន 867361737988403547205962240695953369140625។

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

គុណ 3743906242624487424000000000000000000000000000000 និង 867361737988403547205962240695953369140625 ដើម្បីបាន 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000។

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

គណនាឬសការេនៃ 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 ហើយទទួលបាន 1802032470703125000000000000000000000000000000។

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

គណនា \sqrt[5]{1802032470703125000000000000000000000000000000} ហើយទទួលបាន 1125000000។

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

គណនាស្វ័យគុណ 2 នៃ 36 ហើយបាន 68719476736។

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

គណនាស្វ័យគុណ 3 នៃ 24 ហើយបាន 282429536481។

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

គុណ 68719476736 និង 282429536481 ដើម្បីបាន 19408409961765342806016។

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

គណនាស្វ័យគុណ 5 នៃ 48 ហើយបាន 3552713678800500929355621337890625។

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

គុណ 19408409961765342806016 និង 3552713678800500929355621337890625 ដើម្បីបាន 68952523554931640625000000000000000000000000000000000000។

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

គណនាឬសការេនៃ 68952523554931640625000000000000000000000000000000000000 ហើយទទួលបាន 8303765625000000000000000000។

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

គណនាឬសការេនៃ 8303765625000000000000000000 ហើយទទួលបាន 91125000000000។

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

គណនា \sqrt[3]{91125000000000} ហើយទទួលបាន 45000។

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

ចែក 1125000000 នឹង 45000 ដើម្បីបាន25000។

$$\sqrt{25000}$$

ដាក់ជាកត្តា 25000=50^{2}\times 10។ សរសេរឡើងវិញ​នូវឬសការេនៃផលគុណ \sqrt{50^{2}\times 10} ជាផលគុណ​នៃ​ឬស​ការេ \sqrt{50^{2}}\sqrt{10}។​ យកឬសការ៉េនៃ 50^{2}។

$$50\sqrt{10}$$