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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Ikkalkula 20 bil-power ta' 30 u tikseb 1073741824000000000000000000000000000000.

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

Ikkalkula 3 bil-power ta' 20 u tikseb 3486784401.

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

Immultiplika 1073741824000000000000000000000000000000 u 3486784401 biex tikseb 3743906242624487424000000000000000000000000000000.

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

Ikkalkula 5 bil-power ta' 60 u tikseb 867361737988403547205962240695953369140625.

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

Immultiplika 3743906242624487424000000000000000000000000000000 u 867361737988403547205962240695953369140625 biex tikseb 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000.

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

Ikkalkula l-għerq kwadrat ta' 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 u ikseb 1802032470703125000000000000000000000000000000.

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

Ikkalkola \sqrt[5]{1802032470703125000000000000000000000000000000} u ikseb 1125000000.

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

Ikkalkula 2 bil-power ta' 36 u tikseb 68719476736.

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

Ikkalkula 3 bil-power ta' 24 u tikseb 282429536481.

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

Immultiplika 68719476736 u 282429536481 biex tikseb 19408409961765342806016.

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

Ikkalkula 5 bil-power ta' 48 u tikseb 3552713678800500929355621337890625.

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

Immultiplika 19408409961765342806016 u 3552713678800500929355621337890625 biex tikseb 68952523554931640625000000000000000000000000000000000000.

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

Ikkalkula l-għerq kwadrat ta' 68952523554931640625000000000000000000000000000000000000 u ikseb 8303765625000000000000000000.

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

Ikkalkula l-għerq kwadrat ta' 8303765625000000000000000000 u ikseb 91125000000000.

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

Ikkalkola \sqrt[3]{91125000000000} u ikseb 45000.

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

Iddividi 1125000000 b'45000 biex tikseb25000.

$$\sqrt{25000}$$

Iffattura 25000=50^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{50^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{50^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 50^{2}.

$$50\sqrt{10}$$