sqrt{(2*3^{2}-2^{2}*3)^{2}-4^{2}-(3^{5}:3^{4}+15^{2}:15^2)+2^5-5^5:5^4*7} eching

$$\sqrt { ( 2 \times 3 ^ { 2 } - 2 ^ { 2 } \times 3 ) ^ { 2 } - 4 ^ { 2 } - ( 3 ^ { 5 } : 3 ^ { 4 } + 15 ^ { 2 } : 15 ^ { 2 } ) + 2 ^ { 5 } - 5 ^ { 5 } : 5 ^ { 4 } \times 7 }$$

Baholash

$$\sqrt{13}\approx 3,605551275$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 5 dan 4 ni ayirib, 1 ni oling.

$$\sqrt{\left(2\times 3^{2}-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+\frac{15^{2}}{15^{2}}\right)+2^{5}-\frac{5^{5}}{5^{4}}\times 7}$$

1 ni olish uchun 15^{2} ni 15^{2} ga bo‘ling.

$$\sqrt{\left(2\times 3^{2}-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-\frac{5^{5}}{5^{4}}\times 7}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 5 dan 4 ni ayirib, 1 ni oling.

$$\sqrt{\left(2\times 3^{2}-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

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

$$\sqrt{\left(2\times 9-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

18 hosil qilish uchun 2 va 9 ni ko'paytirish.

$$\sqrt{\left(18-2^{2}\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\sqrt{\left(18-4\times 3\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\sqrt{\left(18-12\right)^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

6 olish uchun 18 dan 12 ni ayirish.

$$\sqrt{6^{2}-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$\sqrt{36-4^{2}-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$\sqrt{36-16-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

20 olish uchun 36 dan 16 ni ayirish.

$$\sqrt{20-\left(3^{1}+1\right)+2^{5}-5^{1}\times 7}$$

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

$$\sqrt{20-\left(3+1\right)+2^{5}-5^{1}\times 7}$$

4 olish uchun 3 va 1'ni qo'shing.

$$\sqrt{20-4+2^{5}-5^{1}\times 7}$$

16 olish uchun 20 dan 4 ni ayirish.

$$\sqrt{16+2^{5}-5^{1}\times 7}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$\sqrt{16+32-5^{1}\times 7}$$

48 olish uchun 16 va 32'ni qo'shing.

$$\sqrt{48-5^{1}\times 7}$$

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

$$\sqrt{48-5\times 7}$$

35 hosil qilish uchun 5 va 7 ni ko'paytirish.

$$\sqrt{48-35}$$

13 olish uchun 48 dan 35 ni ayirish.

$$\sqrt{13}$$