{left(2sqrt{3}+3sqrt{5}right)}^2 eching

$${ \left(2 \sqrt{ 3 } +3 \sqrt{ 5 } \right) }^{ 2 }$$

Baholash

$$12\sqrt{15}+57\approx 103,475800154$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2\sqrt{3}+3\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\sqrt{3}\right)^{2}+12\sqrt{3}\sqrt{5}+9\left(\sqrt{5}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$4\times 3+12\sqrt{3}\sqrt{5}+9\left(\sqrt{5}\right)^{2}$$

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

$$12+12\sqrt{3}\sqrt{5}+9\left(\sqrt{5}\right)^{2}$$

\sqrt{3} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$12+12\sqrt{15}+9\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$12+12\sqrt{15}+9\times 5$$

45 hosil qilish uchun 9 va 5 ni ko'paytirish.

$$12+12\sqrt{15}+45$$

57 olish uchun 12 va 45'ni qo'shing.

$$57+12\sqrt{15}$$

Kengaytirish

$$12 \sqrt{15} + 57 = 103,475800154$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2\sqrt{3}+3\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\sqrt{3}\right)^{2}+12\sqrt{3}\sqrt{5}+9\left(\sqrt{5}\right)^{2}$$

\sqrt{3} kvadrati – 3.

$$4\times 3+12\sqrt{3}\sqrt{5}+9\left(\sqrt{5}\right)^{2}$$

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

$$12+12\sqrt{3}\sqrt{5}+9\left(\sqrt{5}\right)^{2}$$

\sqrt{3} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$12+12\sqrt{15}+9\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$12+12\sqrt{15}+9\times 5$$

45 hosil qilish uchun 9 va 5 ni ko'paytirish.

$$12+12\sqrt{15}+45$$

57 olish uchun 12 va 45'ni qo'shing.

$$57+12\sqrt{15}$$