{left(sqrt{2}-sqrt{3}right)}^2-2sqrt{1/3}*3sqrt{12} eching

$${ \left( \sqrt{ 2 } - \sqrt{ 3 } \right) }^{ 2 } -2 \sqrt{ \frac{ 1 }{ 3 } } \times 3 \sqrt{ 12 }$$

Baholash

$$-2\sqrt{6}-7\approx -11,898979486$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{2}-\sqrt{3}\right)^{2} kengaytirilishi uchun ishlating.

$$\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^{2}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

\sqrt{2} kvadrati – 2.

$$2-2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^{2}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

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

$$2-2\sqrt{6}+\left(\sqrt{3}\right)^{2}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

\sqrt{3} kvadrati – 3.

$$2-2\sqrt{6}+3-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

5 olish uchun 2 va 3'ni qo'shing.

$$5-2\sqrt{6}-2\times 3\sqrt{\frac{1}{3}}\sqrt{12}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$5-2\sqrt{6}-6\sqrt{\frac{1}{3}}\sqrt{12}$$

\sqrt{\frac{1}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$5-2\sqrt{6}-6\times \frac{\sqrt{1}}{\sqrt{3}}\sqrt{12}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$5-2\sqrt{6}-6\times \frac{1}{\sqrt{3}}\sqrt{12}$$

\frac{1}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$5-2\sqrt{6}-6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{12}$$

\sqrt{3} kvadrati – 3.

$$5-2\sqrt{6}-6\times \frac{\sqrt{3}}{3}\sqrt{12}$$

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$5-2\sqrt{6}-6\times \frac{\sqrt{3}}{3}\times 2\sqrt{3}$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$5-2\sqrt{6}-12\times \frac{\sqrt{3}}{3}\sqrt{3}$$

12 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$5-2\sqrt{6}-4\sqrt{3}\sqrt{3}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$5-2\sqrt{6}-4\times 3$$

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

$$5-2\sqrt{6}-12$$

-7 olish uchun 5 dan 12 ni ayirish.

$$-7-2\sqrt{6}$$