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

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

I-evaluate

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

Mga Hakbang ng Solution

Kalkulahin ang 20 sa power ng 30 at kunin ang 1073741824000000000000000000000000000000.

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

Kalkulahin ang 3 sa power ng 20 at kunin ang 3486784401.

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

I-multiply ang 1073741824000000000000000000000000000000 at 3486784401 para makuha ang 3743906242624487424000000000000000000000000000000.

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

Kalkulahin ang 5 sa power ng 60 at kunin ang 867361737988403547205962240695953369140625.

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

I-multiply ang 3743906242624487424000000000000000000000000000000 at 867361737988403547205962240695953369140625 para makuha ang 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000.

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

Kalkulahin ang square root ng 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 at makuha ang 1802032470703125000000000000000000000000000000.

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

Kalkulahin ang \sqrt[5]{1802032470703125000000000000000000000000000000} at makuha ang 1125000000.

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

Kalkulahin ang 2 sa power ng 36 at kunin ang 68719476736.

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

Kalkulahin ang 3 sa power ng 24 at kunin ang 282429536481.

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

I-multiply ang 68719476736 at 282429536481 para makuha ang 19408409961765342806016.

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

Kalkulahin ang 5 sa power ng 48 at kunin ang 3552713678800500929355621337890625.

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

I-multiply ang 19408409961765342806016 at 3552713678800500929355621337890625 para makuha ang 68952523554931640625000000000000000000000000000000000000.

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

Kalkulahin ang square root ng 68952523554931640625000000000000000000000000000000000000 at makuha ang 8303765625000000000000000000.

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

Kalkulahin ang square root ng 8303765625000000000000000000 at makuha ang 91125000000000.

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

Kalkulahin ang \sqrt[3]{91125000000000} at makuha ang 45000.

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

I-divide ang 1125000000 gamit ang 45000 para makuha ang 25000.

$$\sqrt{25000}$$

I-factor out ang 25000=50^{2}\times 10. I-rewrite ang square root ng product na \sqrt{50^{2}\times 10} bilang product ng mga square root na \sqrt{50^{2}}\sqrt{10}. Kunin ang square root ng 50^{2}.

$$50\sqrt{10}$$