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

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

Ebaluatu

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

Ebazpidea

1073741824000000000000000000000000000000 lortzeko, egin 20 ber 30.

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

3486784401 lortzeko, egin 3 ber 20.

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

3743906242624487424000000000000000000000000000000 lortzeko, biderkatu 1073741824000000000000000000000000000000 eta 3486784401.

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

867361737988403547205962240695953369140625 lortzeko, egin 5 ber 60.

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

3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 lortzeko, biderkatu 3743906242624487424000000000000000000000000000000 eta 867361737988403547205962240695953369140625.

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

Kalkulatu 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 balioaren erro karratua eta atera 1802032470703125000000000000000000000000000000.

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

Kalkulatu \sqrt[5]{1802032470703125000000000000000000000000000000} eta atera 1125000000.

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

68719476736 lortzeko, egin 2 ber 36.

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

282429536481 lortzeko, egin 3 ber 24.

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

19408409961765342806016 lortzeko, biderkatu 68719476736 eta 282429536481.

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

3552713678800500929355621337890625 lortzeko, egin 5 ber 48.

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

68952523554931640625000000000000000000000000000000000000 lortzeko, biderkatu 19408409961765342806016 eta 3552713678800500929355621337890625.

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

Kalkulatu 68952523554931640625000000000000000000000000000000000000 balioaren erro karratua eta atera 8303765625000000000000000000.

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

Kalkulatu 8303765625000000000000000000 balioaren erro karratua eta atera 91125000000000.

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

Kalkulatu \sqrt[3]{91125000000000} eta atera 45000.

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

25000 lortzeko, zatitu 1125000000 45000 balioarekin.

$$\sqrt{25000}$$

25000=50^{2}\times 10 faktorea. Berridatzi biderketaren erro karratua (\sqrt{50^{2}\times 10}) \sqrt{50^{2}}\sqrt{10} erro karratuen biderkadura gisa. Atera 50^{2} balioaren erro karratua.

$$50\sqrt{10}$$