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

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

ປະເມີນ

$$\frac{25\times 4096^{\frac{23}{24}}\sqrt[20]{9765625}}{1024}\approx 158,113883008$$

ຂັ້ນຕອນການແກ້

ຄຳນວນ 20 ກຳລັງ 30 ແລະ ໄດ້ 1073741824000000000000000000000000000000.

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

ຄຳນວນ 3 ກຳລັງ 20 ແລະ ໄດ້ 3486784401.

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

ຄູນ 1073741824000000000000000000000000000000 ກັບ 3486784401 ເພື່ອໃຫ້ໄດ້ 3743906242624487424000000000000000000000000000000.

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

ຄຳນວນ 5 ກຳລັງ 60 ແລະ ໄດ້ 867361737988403547205962240695953369140625.

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

ຄູນ 3743906242624487424000000000000000000000000000000 ກັບ 867361737988403547205962240695953369140625 ເພື່ອໃຫ້ໄດ້ 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000.

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

ຄຳນວນຮາກຂອງ 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 ແລະ ໄດ້ 1802032470703125000000000000000000000000000000.

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

ຄຳນວນ \sqrt[5]{1802032470703125000000000000000000000000000000} ແລະ ໄດ້ຮັບ 1125000000.

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

ຄຳນວນ 2 ກຳລັງ 36 ແລະ ໄດ້ 68719476736.

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

ຄຳນວນ 3 ກຳລັງ 24 ແລະ ໄດ້ 282429536481.

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

ຄູນ 68719476736 ກັບ 282429536481 ເພື່ອໃຫ້ໄດ້ 19408409961765342806016.

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

ຄຳນວນ 5 ກຳລັງ 48 ແລະ ໄດ້ 3552713678800500929355621337890625.

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

ຄູນ 19408409961765342806016 ກັບ 3552713678800500929355621337890625 ເພື່ອໃຫ້ໄດ້ 68952523554931640625000000000000000000000000000000000000.

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

ຄຳນວນຮາກຂອງ 68952523554931640625000000000000000000000000000000000000 ແລະ ໄດ້ 8303765625000000000000000000.

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

ຄຳນວນຮາກຂອງ 8303765625000000000000000000 ແລະ ໄດ້ 91125000000000.

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

ຄຳນວນ \sqrt[3]{91125000000000} ແລະ ໄດ້ຮັບ 45000.

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

ຫານ 1125000000 ດ້ວຍ 45000 ເພື່ອໄດ້ 25000.

$$\sqrt{25000}$$

ຕົວປະກອບ 25000=50^{2}\times 10. ຂຽນຮາກຂັ້ນສອງຂອງຜົນຄູນ \sqrt{50^{2}\times 10} ເປັນຜົນຄູນຂອງຮາກຂັ້ນສອງ \sqrt{50^{2}}\sqrt{10}. ເອົາຮາກຂັ້ນສອງຂອງ 50^{2}.

$$50\sqrt{10}$$