Atrisiniet 6*62*6*10^-24/sqrt{2*167*10^-27*81*9*10^-16}

$$\frac { 6 \cdot 62 \cdot 6 \times 10 ^ { - 24 } } { \sqrt { 2 \times 167 \times 10 ^ { - 27 } \times 81 \cdot 9 \times 10 ^ { - 16 } } }$$

Izrēķināt

$$\frac{31\sqrt{835}}{62625}\approx 0,01430399$$

Atrisinājuma darbības

Lai reizinātu vienas bāzes pakāpes, saskaitiet kāpinātājus. Saskaitiet -27 un -16, lai iegūtu -43.

$$\frac{6\times 62\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Reiziniet 6 un 62, lai iegūtu 372.

$$\frac{372\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Reiziniet 372 un 6, lai iegūtu 2232.

$$\frac{2232\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Aprēķiniet 10 pakāpē -24 un iegūstiet \frac{1}{1000000000000000000000000}.

$$\frac{2232\times \frac{1}{1000000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Reiziniet 2232 un \frac{1}{1000000000000000000000000}, lai iegūtu \frac{279}{125000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Reiziniet 2 un 167, lai iegūtu 334.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times 10^{-43}\times 81\times 9}}$$

Aprēķiniet 10 pakāpē -43 un iegūstiet \frac{1}{10000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times \frac{1}{10000000000000000000000000000000000000000000}\times 81\times 9}}$$

Reiziniet 334 un \frac{1}{10000000000000000000000000000000000000000000}, lai iegūtu \frac{167}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{167}{5000000000000000000000000000000000000000000}\times 81\times 9}}$$

Reiziniet \frac{167}{5000000000000000000000000000000000000000000} un 81, lai iegūtu \frac{13527}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{13527}{5000000000000000000000000000000000000000000}\times 9}}$$

Reiziniet \frac{13527}{5000000000000000000000000000000000000000000} un 9, lai iegūtu \frac{121743}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{121743}{5000000000000000000000000000000000000000000}}}$$

Pārrakstiet dalījuma kvadrātsakni \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} kā kvadrātveida saknes \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

Sadaliet reizinātājos 121743=27^{2}\times 167. Pārrakstiet reizinājuma kvadrātsakni \sqrt{27^{2}\times 167} kā kvadrātveida saknes \sqrt{27^{2}}\sqrt{167}. Izvelciet kvadrātsakni no 27^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

Sadaliet reizinātājos 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Pārrakstiet reizinājuma kvadrātsakni \sqrt{1000000000000000000000^{2}\times 5} kā kvadrātveida saknes \sqrt{1000000000000000000000^{2}}\sqrt{5}. Izvelciet kvadrātsakni no 1000000000000000000000^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}}}$$

Atbrīvojieties no iracionalitātes saucēju ar \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}}, reizinot skaitītāju un saucēju ar \sqrt{5}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

Skaitļa \sqrt{5} kvadrāts ir 5.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\times 5}}$$

Lai reiziniet \sqrt{167} un \sqrt{5}, reiziniet numurus zem kvadrātveida saknes.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{1000000000000000000000\times 5}}$$

Reiziniet 1000000000000000000000 un 5, lai iegūtu 5000000000000000000000.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{5000000000000000000000}}$$

Daliet \frac{279}{125000000000000000000000} ar \frac{27\sqrt{835}}{5000000000000000000000}, reizinot \frac{279}{125000000000000000000000} ar apgriezto daļskaitli \frac{27\sqrt{835}}{5000000000000000000000} .

$$\frac{279\times 5000000000000000000000}{125000000000000000000000\times 27\sqrt{835}}$$

Saīsiniet 9\times 5000000000000000000000 gan skaitītājā, gan saucējā.

$$\frac{31}{3\times 25\sqrt{835}}$$

Atbrīvojieties no iracionalitātes saucēju ar \frac{31}{3\times 25\sqrt{835}}, reizinot skaitītāju un saucēju ar \sqrt{835}.

$$\frac{31\sqrt{835}}{3\times 25\left(\sqrt{835}\right)^{2}}$$

Skaitļa \sqrt{835} kvadrāts ir 835.

$$\frac{31\sqrt{835}}{3\times 25\times 835}$$

Reiziniet 3 un 25, lai iegūtu 75.

$$\frac{31\sqrt{835}}{75\times 835}$$

Reiziniet 75 un 835, lai iegūtu 62625.

$$\frac{31\sqrt{835}}{62625}$$