sqrt{6.607*10^-11*5.98*10^24/900+6378} eching

$$\sqrt { \frac { 6.607 \cdot 10 ^ { - 11 } \cdot 5.98 \cdot 10 ^ { 24 } } { 900 + 6378 } }$$

Baholash

$$\frac{10000\sqrt{7188819027}}{3639}\approx 232995,063558778$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -11 va 24 ni qo‘shib, 13 ni oling.

$$\sqrt{\frac{6,607\times 10^{13}\times 5,98}{900+6378}}$$

13 daraja ko‘rsatkichini 10 ga hisoblang va 10000000000000 ni qiymatni oling.

$$\sqrt{\frac{6,607\times 10000000000000\times 5,98}{900+6378}}$$

66070000000000 hosil qilish uchun 6,607 va 10000000000000 ni ko'paytirish.

$$\sqrt{\frac{66070000000000\times 5,98}{900+6378}}$$

395098600000000 hosil qilish uchun 66070000000000 va 5,98 ni ko'paytirish.

$$\sqrt{\frac{395098600000000}{900+6378}}$$

7278 olish uchun 900 va 6378'ni qo'shing.

$$\sqrt{\frac{395098600000000}{7278}}$$

\frac{395098600000000}{7278} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{197549300000000}{3639}}$$

\sqrt{\frac{197549300000000}{3639}} boʻlinmasining kvadrat ildizini \frac{\sqrt{197549300000000}}{\sqrt{3639}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{197549300000000}}{\sqrt{3639}}$$

Faktor: 197549300000000=10000^{2}\times 1975493. \sqrt{10000^{2}\times 1975493} koʻpaytmasining kvadrat ildizini \sqrt{10000^{2}}\sqrt{1975493} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 10000^{2} ning kvadrat ildizini chiqarish.

$$\frac{10000\sqrt{1975493}}{\sqrt{3639}}$$

\frac{10000\sqrt{1975493}}{\sqrt{3639}} maxrajini \sqrt{3639} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{10000\sqrt{1975493}\sqrt{3639}}{\left(\sqrt{3639}\right)^{2}}$$

\sqrt{3639} kvadrati – 3639.

$$\frac{10000\sqrt{1975493}\sqrt{3639}}{3639}$$

\sqrt{1975493} va \sqrt{3639} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{10000\sqrt{7188819027}}{3639}$$