4^2/3^2*2sqrt{5}*6= eching

$$\frac{ { 4 }^{ 2 } }{ { 3 }^{ 2 } \times 2 \sqrt{ 5 } } \times 6=$$

Baholash

$$\frac{16\sqrt{5}}{15}\approx 2,385139176$$

Yechim qadamlari

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$6\times \frac{16}{2\times 3^{2}\sqrt{5}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$6\times \frac{16}{2\times 9\sqrt{5}}$$

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

$$6\times \frac{16}{18\sqrt{5}}$$

\frac{16}{18\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$6\times \frac{16\sqrt{5}}{18\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$6\times \frac{16\sqrt{5}}{18\times 5}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$6\times \frac{8\sqrt{5}}{5\times 9}$$

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

$$6\times \frac{8\sqrt{5}}{45}$$

6\times \frac{8\sqrt{5}}{45} ni yagona kasrga aylantiring.

$$\frac{6\times 8\sqrt{5}}{45}$$

48 hosil qilish uchun 6 va 8 ni ko'paytirish.

$$\frac{48\sqrt{5}}{45}$$

\frac{16}{15}\sqrt{5} ni olish uchun 48\sqrt{5} ni 45 ga bo‘ling.

$$\frac{16}{15}\sqrt{5}$$