Ratkaise 4*pi^2*left(228*10^8right)^3divleft(687*24*60*60right)^2/372*{6794^2div4}

$$\frac{ 4 \times { \pi }^{ 2 } \times { \left(228 \times { 10 }^{ 8 } \right) }^{ 3 } \div { \left(687 \times 24 \times 60 \times 60 \right) }^{ 2 } }{ 372 \times { 6794 }^{ 2 } \div 4 }$$

Laske

$$\frac{42868750000000000000000\pi ^{2}}{13675754015223831}\approx 30937789,843119998$$

Ratkaisun vaiheet

Jaa \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} luvulla \frac{372\times 6794^{2}}{4} kertomalla \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} luvun \frac{372\times 6794^{2}}{4} käänteisluvulla.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 372\times 6794^{2}}$$

Supista 4 sekä osoittajasta että nimittäjästä.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Laske 10 potenssiin 8, jolloin ratkaisuksi tulee 100000000.

$$\frac{4\pi ^{2}\times \left(228\times 100000000\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 228 ja 100000000, niin saadaan 22800000000.

$$\frac{4\pi ^{2}\times 22800000000^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Laske 22800000000 potenssiin 3, jolloin ratkaisuksi tulee 11852352000000000000000000000000.

$$\frac{4\pi ^{2}\times 11852352000000000000000000000000}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 4 ja 11852352000000000000000000000000, niin saadaan 47409408000000000000000000000000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Laske 6794 potenssiin 2, jolloin ratkaisuksi tulee 46158436.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 46158436\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 93 ja 46158436, niin saadaan 4292734548.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 24 ja 60, niin saadaan 1440.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(1440\times 60\times 687\right)^{2}}$$

Kerro 1440 ja 60, niin saadaan 86400.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(86400\times 687\right)^{2}}$$

Kerro 86400 ja 687, niin saadaan 59356800.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 59356800^{2}}$$

Laske 59356800 potenssiin 2, jolloin ratkaisuksi tulee 3523229706240000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 3523229706240000}$$

Kerro 4292734548 ja 3523229706240000, niin saadaan 15124289880516339179520000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{15124289880516339179520000}$$

Jaa 47409408000000000000000000000000\pi ^{2} luvulla 15124289880516339179520000, jolloin ratkaisuksi tulee \frac{42868750000000000000000}{13675754015223831}\pi ^{2}.

$$\frac{42868750000000000000000}{13675754015223831}\pi ^{2}$$

Lavenna

$$\frac{42868750000000000000000 \pi ^ {2}}{13675754015223831} = 30937789\frac{11530301708766792}{13675754015223832} = 30937789,843119998$$

Ratkaisun vaiheet

Jaa \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} luvulla \frac{372\times 6794^{2}}{4} kertomalla \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} luvun \frac{372\times 6794^{2}}{4} käänteisluvulla.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 372\times 6794^{2}}$$

Supista 4 sekä osoittajasta että nimittäjästä.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Laske 10 potenssiin 8, jolloin ratkaisuksi tulee 100000000.

$$\frac{4\pi ^{2}\times \left(228\times 100000000\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 228 ja 100000000, niin saadaan 22800000000.

$$\frac{4\pi ^{2}\times 22800000000^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Laske 22800000000 potenssiin 3, jolloin ratkaisuksi tulee 11852352000000000000000000000000.

$$\frac{4\pi ^{2}\times 11852352000000000000000000000000}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 4 ja 11852352000000000000000000000000, niin saadaan 47409408000000000000000000000000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Laske 6794 potenssiin 2, jolloin ratkaisuksi tulee 46158436.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 46158436\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 93 ja 46158436, niin saadaan 4292734548.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Kerro 24 ja 60, niin saadaan 1440.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(1440\times 60\times 687\right)^{2}}$$

Kerro 1440 ja 60, niin saadaan 86400.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(86400\times 687\right)^{2}}$$

Kerro 86400 ja 687, niin saadaan 59356800.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 59356800^{2}}$$

Laske 59356800 potenssiin 2, jolloin ratkaisuksi tulee 3523229706240000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 3523229706240000}$$

Kerro 4292734548 ja 3523229706240000, niin saadaan 15124289880516339179520000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{15124289880516339179520000}$$

Jaa 47409408000000000000000000000000\pi ^{2} luvulla 15124289880516339179520000, jolloin ratkaisuksi tulee \frac{42868750000000000000000}{13675754015223831}\pi ^{2}.

$$\frac{42868750000000000000000}{13675754015223831}\pi ^{2}$$