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

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

Arvuta

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

Lahenduse etapid

Arvutage 30 aste 20 ja leidke 1073741824000000000000000000000000000000.

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

Arvutage 20 aste 3 ja leidke 3486784401.

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

Korrutage 1073741824000000000000000000000000000000 ja 3486784401, et leida 3743906242624487424000000000000000000000000000000.

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

Arvutage 60 aste 5 ja leidke 867361737988403547205962240695953369140625.

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

Korrutage 3743906242624487424000000000000000000000000000000 ja 867361737988403547205962240695953369140625, et leida 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000.

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

Arvutage 3247321025468409061431884765625000000000000000000000000000000000000000000000000000000000000 ruutjuur, et saada 1802032470703125000000000000000000000000000000.

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

Arvutage \sqrt[5]{1802032470703125000000000000000000000000000000}, et saada 1125000000.

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

Arvutage 36 aste 2 ja leidke 68719476736.

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

Arvutage 24 aste 3 ja leidke 282429536481.

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

Korrutage 68719476736 ja 282429536481, et leida 19408409961765342806016.

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

Arvutage 48 aste 5 ja leidke 3552713678800500929355621337890625.

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

Korrutage 19408409961765342806016 ja 3552713678800500929355621337890625, et leida 68952523554931640625000000000000000000000000000000000000.

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

Arvutage 68952523554931640625000000000000000000000000000000000000 ruutjuur, et saada 8303765625000000000000000000.

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

Arvutage 8303765625000000000000000000 ruutjuur, et saada 91125000000000.

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

Arvutage \sqrt[3]{91125000000000}, et saada 45000.

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

Jagage 1125000000 väärtusega 45000, et leida 25000.

$$\sqrt{25000}$$

Tegurda 25000=50^{2}\times 10. Kirjutage \sqrt{50^{2}\times 10} toote juured, kui see ruut \sqrt{50^{2}}\sqrt{10}. Leidke 50^{2} ruutjuur.

$$50\sqrt{10}$$