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

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

मूल्यांकन करचें

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

सोडोवणी पांवडे

1073741824000000000000000000000000000000 मेळोवंक 30 चो 20 पॉवर मेजचो.

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

3486784401 मेळोवंक 20 चो 3 पॉवर मेजचो.

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

3743906242624487424000000000000000000000000000000 मेळोवंक 1073741824000000000000000000000000000000 आनी 3486784401 गुणचें.

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

867361737988403547205962240695953369140625 मेळोवंक 60 चो 5 पॉवर मेजचो.

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

3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 मेळोवंक 3743906242624487424000000000000000000000000000000 आनी 867361737988403547205962240695953369140625 गुणचें.

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

3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 चें वर्गमूळ मेजचें आनी 1802032470703125000000000000000000000000000000 मेळोवचें.

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

\sqrt[5]{1802032470703125000000000000000000000000000000} मेजचो आनी 1125000000 मेळोवचो.

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

68719476736 मेळोवंक 36 चो 2 पॉवर मेजचो.

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

282429536481 मेळोवंक 24 चो 3 पॉवर मेजचो.

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

19408409961765342806016 मेळोवंक 68719476736 आनी 282429536481 गुणचें.

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

3552713678800500929355621337890625 मेळोवंक 48 चो 5 पॉवर मेजचो.

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

68952523554931640625000000000000000000000000000000000000 मेळोवंक 19408409961765342806016 आनी 3552713678800500929355621337890625 गुणचें.

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

68952523554931640625000000000000000000000000000000000000 चें वर्गमूळ मेजचें आनी 8303765625000000000000000000 मेळोवचें.

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

8303765625000000000000000000 चें वर्गमूळ मेजचें आनी 91125000000000 मेळोवचें.

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

\sqrt[3]{91125000000000} मेजचो आनी 45000 मेळोवचो.

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

25000 मेळोवंक 1125000000 क 45000 न भाग लावचो.

$$\sqrt{25000}$$

25000=50^{2}\times 10 गुणकपद काडचें. \sqrt{50^{2}}\sqrt{10} च्या वर्ग मूळाचो गुणाकार म्हूण \sqrt{50^{2}\times 10} च्या वर्गमूळाचो गुणाकार परत बरोवचो. 50^{2} चें वर्गमूळ घेवचें.

$$50\sqrt{10}$$