sqrt{3}(sqrt{2}-sqrt{3})^2 eching

$$\sqrt { 3 } ( \sqrt { 2 } - \sqrt { 3 } ) ^ { 2 }$$

Baholash

$$5\sqrt{3}-6\sqrt{2}\approx 0,174972664$$

Yechim qadamlari

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

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

\sqrt{2} kvadrati – 2.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

$$\sqrt{3}\left(5-2\sqrt{6}\right)$$

\sqrt{3} ga 5-2\sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Faktor: 6=3\times 2. \sqrt{3\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

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

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

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

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

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