sqrt{frac{3^{10}*5^{7}*8^{3}*1^{20}*25}{2^{6}*5^2*3^8*5^7*2^3}} eching

$$\sqrt { \frac { 3 ^ { 10 } \cdot 5 ^ { 7 } \cdot 8 ^ { 3 } \cdot 1 ^ { 20 } \cdot 25 } { 2 ^ { 6 } \cdot 5 ^ { 2 } \cdot 3 ^ { 8 } \cdot 5 ^ { 7 } \cdot 2 ^ { 3 } } }$$

Baholash

$$3$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va 3 ni qo‘shib, 9 ni oling.

$$\sqrt{\frac{3^{10}\times 5^{7}\times 8^{3}\times 1^{20}\times 25}{2^{9}\times 5^{2}\times 3^{8}\times 5^{7}}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 7 ni qo‘shib, 9 ni oling.

$$\sqrt{\frac{3^{10}\times 5^{7}\times 8^{3}\times 1^{20}\times 25}{2^{9}\times 5^{9}\times 3^{8}}}$$

Surat va maxrajdagi ikkala 3^{8}\times 5^{7} ni qisqartiring.

$$\sqrt{\frac{25\times 1^{20}\times 3^{2}\times 8^{3}}{2^{9}\times 5^{2}}}$$

20 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\sqrt{\frac{25\times 1\times 3^{2}\times 8^{3}}{2^{9}\times 5^{2}}}$$

25 hosil qilish uchun 25 va 1 ni ko'paytirish.

$$\sqrt{\frac{25\times 3^{2}\times 8^{3}}{2^{9}\times 5^{2}}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\sqrt{\frac{25\times 9\times 8^{3}}{2^{9}\times 5^{2}}}$$

225 hosil qilish uchun 25 va 9 ni ko'paytirish.

$$\sqrt{\frac{225\times 8^{3}}{2^{9}\times 5^{2}}}$$

3 daraja ko‘rsatkichini 8 ga hisoblang va 512 ni qiymatni oling.

$$\sqrt{\frac{225\times 512}{2^{9}\times 5^{2}}}$$

115200 hosil qilish uchun 225 va 512 ni ko'paytirish.

$$\sqrt{\frac{115200}{2^{9}\times 5^{2}}}$$

9 daraja ko‘rsatkichini 2 ga hisoblang va 512 ni qiymatni oling.

$$\sqrt{\frac{115200}{512\times 5^{2}}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\sqrt{\frac{115200}{512\times 25}}$$

12800 hosil qilish uchun 512 va 25 ni ko'paytirish.

$$\sqrt{\frac{115200}{12800}}$$

9 ni olish uchun 115200 ni 12800 ga bo‘ling.

$$\sqrt{9}$$

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

$$3$$

Omil

$$3$$