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

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

Baholash

$$30-12\sqrt{6}\approx 0,606123087$$

Yechim qadamlari

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

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

\sqrt{2} kvadrati – 2.

$$9\times 2-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

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

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

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

$$18-12\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$18-12\sqrt{6}+4\times 3$$

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

$$18-12\sqrt{6}+12$$

30 olish uchun 18 va 12'ni qo'shing.

$$30-12\sqrt{6}$$

Kengaytirish

$$30-12\sqrt{6}$$

Yechim qadamlari

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

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

\sqrt{2} kvadrati – 2.

$$9\times 2-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

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

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

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

$$18-12\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$18-12\sqrt{6}+4\times 3$$

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

$$18-12\sqrt{6}+12$$

30 olish uchun 18 va 12'ni qo'shing.

$$30-12\sqrt{6}$$