sqrt{4/3*55*10^-9*667*10^-11*314} eching

$$\sqrt { \frac { 4 } { 3 } \times 55 \times 10 ^ { - 9 } \times 667 \times 10 ^ { - 11 } \times 314 }$$

Baholash

$$\frac{\sqrt{34557270}}{15000000000}\approx 0,000000392$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -9 va -11 ni qo‘shib, -20 ni oling.

$$\sqrt{\frac{4}{3}\times 55\times 10^{-20}\times 667\times 314}$$

\frac{220}{3} hosil qilish uchun \frac{4}{3} va 55 ni ko'paytirish.

$$\sqrt{\frac{220}{3}\times 10^{-20}\times 667\times 314}$$

-20 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{100000000000000000000} ni qiymatni oling.

$$\sqrt{\frac{220}{3}\times \frac{1}{100000000000000000000}\times 667\times 314}$$

\frac{11}{15000000000000000000} hosil qilish uchun \frac{220}{3} va \frac{1}{100000000000000000000} ni ko'paytirish.

$$\sqrt{\frac{11}{15000000000000000000}\times 667\times 314}$$

\frac{7337}{15000000000000000000} hosil qilish uchun \frac{11}{15000000000000000000} va 667 ni ko'paytirish.

$$\sqrt{\frac{7337}{15000000000000000000}\times 314}$$

\frac{1151909}{7500000000000000000} hosil qilish uchun \frac{7337}{15000000000000000000} va 314 ni ko'paytirish.

$$\sqrt{\frac{1151909}{7500000000000000000}}$$

\sqrt{\frac{1151909}{7500000000000000000}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1151909}}{\sqrt{7500000000000000000}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}$$

Faktor: 7500000000000000000=500000000^{2}\times 30. \sqrt{500000000^{2}\times 30} koʻpaytmasining kvadrat ildizini \sqrt{500000000^{2}}\sqrt{30} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 500000000^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{1151909}}{500000000\sqrt{30}}$$

\frac{\sqrt{1151909}}{500000000\sqrt{30}} maxrajini \sqrt{30} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\left(\sqrt{30}\right)^{2}}$$

\sqrt{30} kvadrati – 30.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\times 30}$$

\sqrt{1151909} va \sqrt{30} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{34557270}}{500000000\times 30}$$

15000000000 hosil qilish uchun 500000000 va 30 ni ko'paytirish.

$$\frac{\sqrt{34557270}}{15000000000}$$