2^3-2(2+sqrt{3}+sqrt{2}*2sqrt{3}-sqrt{32}-sqrt{3}-sqrt{2}) eching

$$2 ^ { 3 } - 2 ( 2 + \sqrt { 3 } + \sqrt { 2 } \cdot 2 \sqrt { 3 } - \sqrt { 32 } - \sqrt { 3 } - \sqrt { 2 } )$$

Baholash

$$10\sqrt{2}+4-4\sqrt{6}\approx 8,344176653$$

Yechim qadamlari

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$8-2\left(2+\sqrt{3}+2\sqrt{2}\sqrt{3}-\sqrt{32}-\sqrt{3}-\sqrt{2}\right)$$

\sqrt{2} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$8-2\left(2+\sqrt{3}+2\sqrt{6}-\sqrt{32}-\sqrt{3}-\sqrt{2}\right)$$

Faktor: 32=4^{2}\times 2. \sqrt{4^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$8-2\left(2+\sqrt{3}+2\sqrt{6}-4\sqrt{2}-\sqrt{3}-\sqrt{2}\right)$$

0 ni olish uchun \sqrt{3} va -\sqrt{3} ni birlashtirish.

$$8-2\left(2+2\sqrt{6}-4\sqrt{2}-\sqrt{2}\right)$$

-5\sqrt{2} ni olish uchun -4\sqrt{2} va -\sqrt{2} ni birlashtirish.

$$8-2\left(2+2\sqrt{6}-5\sqrt{2}\right)$$

-2 ga 2+2\sqrt{6}-5\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8-4-4\sqrt{6}+10\sqrt{2}$$

4 olish uchun 8 dan 4 ni ayirish.

$$4-4\sqrt{6}+10\sqrt{2}$$

Omil

$$2 {(5 \sqrt{2} + 2 - 2 \sqrt{6})} = 8,344176653$$