sqrt{3*6626*10^-34/8*91*10^-28*2*10^14} eching

$$\sqrt{ \frac{ 3 \times 6626 \times { 10 }^{ -34 } }{ 8 \times 91 \times { 10 }^{ -28 } \times 2 \times { 10 }^{ 14 } } }$$

Baholash

$$\frac{\sqrt{1808898}}{3640000000000}\approx 3,69492524 \cdot 10^{-10}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -28 va 14 ni qo‘shib, -14 ni oling.

$$\sqrt{\frac{3\times 6626\times 10^{-34}}{8\times 91\times 10^{-14}\times 2}}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\sqrt{\frac{3\times 3313\times 10^{-34}}{2\times 4\times 91\times 10^{-14}}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\sqrt{\frac{3\times 3313}{2\times 4\times 91\times 10^{20}}}$$

9939 hosil qilish uchun 3 va 3313 ni ko'paytirish.

$$\sqrt{\frac{9939}{2\times 4\times 91\times 10^{20}}}$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$\sqrt{\frac{9939}{8\times 91\times 10^{20}}}$$

728 hosil qilish uchun 8 va 91 ni ko'paytirish.

$$\sqrt{\frac{9939}{728\times 10^{20}}}$$

20 daraja ko‘rsatkichini 10 ga hisoblang va 100000000000000000000 ni qiymatni oling.

$$\sqrt{\frac{9939}{728\times 100000000000000000000}}$$

72800000000000000000000 hosil qilish uchun 728 va 100000000000000000000 ni ko'paytirish.

$$\sqrt{\frac{9939}{72800000000000000000000}}$$

\sqrt{\frac{9939}{72800000000000000000000}} boʻlinmasining kvadrat ildizini \frac{\sqrt{9939}}{\sqrt{72800000000000000000000}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{9939}}{\sqrt{72800000000000000000000}}$$

Faktor: 72800000000000000000000=20000000000^{2}\times 182. \sqrt{20000000000^{2}\times 182} koʻpaytmasining kvadrat ildizini \sqrt{20000000000^{2}}\sqrt{182} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 20000000000^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{9939}}{20000000000\sqrt{182}}$$

\frac{\sqrt{9939}}{20000000000\sqrt{182}} maxrajini \sqrt{182} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{9939}\sqrt{182}}{20000000000\left(\sqrt{182}\right)^{2}}$$

\sqrt{182} kvadrati – 182.

$$\frac{\sqrt{9939}\sqrt{182}}{20000000000\times 182}$$

\sqrt{9939} va \sqrt{182} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{1808898}}{20000000000\times 182}$$

3640000000000 hosil qilish uchun 20000000000 va 182 ni ko'paytirish.

$$\frac{\sqrt{1808898}}{3640000000000}$$