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

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

ھېسابلاش

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

يېشىش باسقۇچلىرى

20 نىڭ 30-دەرىجىسىنى ھېسابلاپ 1073741824000000000000000000000000000000 نى چىقىرىڭ.

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

3 نىڭ 20-دەرىجىسىنى ھېسابلاپ 3486784401 نى چىقىرىڭ.

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

1073741824000000000000000000000000000000 گە 3486784401 نى كۆپەيتىپ 3743906242624487424000000000000000000000000000000 نى چىقىرىڭ.

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

5 نىڭ 60-دەرىجىسىنى ھېسابلاپ 867361737988403547205962240695953369140625 نى چىقىرىڭ.

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

3743906242624487424000000000000000000000000000000 گە 867361737988403547205962240695953369140625 نى كۆپەيتىپ 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 نى چىقىرىڭ.

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

3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 نىڭ كىۋادرات يىلتىزىنى ھېسابلاپ، 1802032470703125000000000000000000000000000000 نى چىقىرىڭ.

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

\sqrt[5]{1802032470703125000000000000000000000000000000} نى ھېسابلاپ، 1125000000 نى چىقىرىڭ.

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

2 نىڭ 36-دەرىجىسىنى ھېسابلاپ 68719476736 نى چىقىرىڭ.

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

3 نىڭ 24-دەرىجىسىنى ھېسابلاپ 282429536481 نى چىقىرىڭ.

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

68719476736 گە 282429536481 نى كۆپەيتىپ 19408409961765342806016 نى چىقىرىڭ.

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

5 نىڭ 48-دەرىجىسىنى ھېسابلاپ 3552713678800500929355621337890625 نى چىقىرىڭ.

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

19408409961765342806016 گە 3552713678800500929355621337890625 نى كۆپەيتىپ 68952523554931640625000000000000000000000000000000000000 نى چىقىرىڭ.

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

68952523554931640625000000000000000000000000000000000000 نىڭ كىۋادرات يىلتىزىنى ھېسابلاپ، 8303765625000000000000000000 نى چىقىرىڭ.

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

8303765625000000000000000000 نىڭ كىۋادرات يىلتىزىنى ھېسابلاپ، 91125000000000 نى چىقىرىڭ.

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

\sqrt[3]{91125000000000} نى ھېسابلاپ، 45000 نى چىقىرىڭ.

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

1125000000 نى 45000 گە بۆلۈپ 25000 نى چىقىرىڭ.

$$\sqrt{25000}$$

25000=50^{2}\times 10 نى ئاجرىتىڭ. ھاسىلات \sqrt{50^{2}\times 10} نىڭ كىۋادرات يىلتىزىنى كىۋادرات يىلتىز \sqrt{50^{2}}\sqrt{10} نىڭ ھاسىلاتى شەكلىدە قايتا يېزىڭ. 50^{2} نىڭ كىۋادرات يىلتىزىنى چىقىرىڭ.

$$50\sqrt{10}$$