{left(2sqrt{6}+sqrt{5}right)}^2 eching

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

Baholash

$$4\sqrt{30}+29\approx 50,9089023$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2\sqrt{6}+\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\sqrt{6}\right)^{2}+4\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

\sqrt{6} kvadrati – 6.

$$4\times 6+4\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$24+4\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

\sqrt{6} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$24+4\sqrt{30}+\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$24+4\sqrt{30}+5$$

29 olish uchun 24 va 5'ni qo'shing.

$$29+4\sqrt{30}$$

Kengaytirish

$$4 \sqrt{30} + 29 = 50,9089023$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2\sqrt{6}+\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.

$$4\left(\sqrt{6}\right)^{2}+4\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

\sqrt{6} kvadrati – 6.

$$4\times 6+4\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$24+4\sqrt{6}\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

\sqrt{6} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$24+4\sqrt{30}+\left(\sqrt{5}\right)^{2}$$

\sqrt{5} kvadrati – 5.

$$24+4\sqrt{30}+5$$

29 olish uchun 24 va 5'ni qo'shing.

$$29+4\sqrt{30}$$