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

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

Baholash

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

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -27 va -16 ni qo‘shib, -43 ni oling.

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

372 hosil qilish uchun 6 va 62 ni ko'paytirish.

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

2232 hosil qilish uchun 372 va 6 ni ko'paytirish.

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

-24 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000000000000000000000} ni qiymatni oling.

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

\frac{279}{125000000000000000000000} hosil qilish uchun 2232 va \frac{1}{1000000000000000000000000} ni ko'paytirish.

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

334 hosil qilish uchun 2 va 167 ni ko'paytirish.

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

-43 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000000000000000000000000000000000000000000} ni qiymatni oling.

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

\frac{167}{5000000000000000000000000000000000000000000} hosil qilish uchun 334 va \frac{1}{10000000000000000000000000000000000000000000} ni ko'paytirish.

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

\frac{13527}{5000000000000000000000000000000000000000000} hosil qilish uchun \frac{167}{5000000000000000000000000000000000000000000} va 81 ni ko'paytirish.

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

\frac{121743}{5000000000000000000000000000000000000000000} hosil qilish uchun \frac{13527}{5000000000000000000000000000000000000000000} va 9 ni ko'paytirish.

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

\sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} boʻlinmasining kvadrat ildizini \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

Faktor: 121743=27^{2}\times 167. \sqrt{27^{2}\times 167} koʻpaytmasining kvadrat ildizini \sqrt{27^{2}}\sqrt{167} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 27^{2} ning kvadrat ildizini chiqarish.

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

Faktor: 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. \sqrt{1000000000000000000000^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{1000000000000000000000^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 1000000000000000000000^{2} ning kvadrat ildizini chiqarish.

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

\frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{5} kvadrati – 5.

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

\sqrt{167} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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

5000000000000000000000 hosil qilish uchun 1000000000000000000000 va 5 ni ko'paytirish.

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

\frac{279}{125000000000000000000000} ni \frac{27\sqrt{835}}{5000000000000000000000} ga bo'lish \frac{279}{125000000000000000000000} ga k'paytirish \frac{27\sqrt{835}}{5000000000000000000000} ga qaytarish.

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

Surat va maxrajdagi ikkala 9\times 5000000000000000000000 ni qisqartiring.

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

\frac{31}{3\times 25\sqrt{835}} maxrajini \sqrt{835} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{835} kvadrati – 835.

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

75 hosil qilish uchun 3 va 25 ni ko'paytirish.

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

62625 hosil qilish uchun 75 va 835 ni ko'paytirish.

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