2/sqrt{5}frac{1sqrt{3}}{2}-1/sqrt{5}1/2 eching

$$\frac{ 2 }{ \sqrt{ 5 } } \frac{ 1 \sqrt{ 3 } }{ 2 } - \frac{ 1 }{ \sqrt{ 5 } } \frac{ 1 }{ 2 }$$

Baholash

$$\frac{\sqrt{15}}{5}-\frac{\sqrt{5}}{10}\approx 0,550989871$$

Qisqa yechim qadamlari

\frac{2}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{1\sqrt{3}}{2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

\sqrt{5} kvadrati – 5.

$$\frac{2\sqrt{5}}{5}\times \frac{1\sqrt{3}}{2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2\sqrt{5}}{5} ni \frac{1\sqrt{3}}{2} ga ko‘paytiring.

$$\frac{2\sqrt{5}\times 1\sqrt{3}}{5\times 2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

\frac{1}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{1}{2}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}}{5}\times \frac{1}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{5}}{5} ni \frac{1}{2} ga ko‘paytiring.

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

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}}{10}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 va 10 ning eng kichik umumiy karralisi 10. \frac{\sqrt{3}\sqrt{5}}{5} ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{2\sqrt{3}\sqrt{5}}{10}-\frac{\sqrt{5}}{10}$$

\frac{2\sqrt{3}\sqrt{5}}{10} va \frac{\sqrt{5}}{10} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2\sqrt{3}\sqrt{5}-\sqrt{5}}{10}$$

2\sqrt{3}\sqrt{5}-\sqrt{5} ichidagi ko‘paytirishlarni bajaring.

$$\frac{2\sqrt{15}-\sqrt{5}}{10}$$

Omil

$$\frac{\sqrt{5} {(2 \sqrt{3} - 1)}}{10} = 0,5509898714915045$$