1/2sqrt{2+sqrt{5}} eching

$$\frac { 1 } { 2 \sqrt { 2 } + \sqrt { 5 } }$$

Baholash

$$\frac{2\sqrt{2}-\sqrt{5}}{3}\approx 0,197453049$$

Yechim qadamlari

\frac{1}{2\sqrt{2}+\sqrt{5}} maxrajini 2\sqrt{2}-\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{2}-\sqrt{5}}{\left(2\sqrt{2}+\sqrt{5}\right)\left(2\sqrt{2}-\sqrt{5}\right)}$$

Hisoblang: \left(2\sqrt{2}+\sqrt{5}\right)\left(2\sqrt{2}-\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(2\sqrt{2}\right)^{2} ni kengaytirish.

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

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

$$\frac{2\sqrt{2}-\sqrt{5}}{4\left(\sqrt{2}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{2\sqrt{2}-\sqrt{5}}{4\times 2-\left(\sqrt{5}\right)^{2}}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{2\sqrt{2}-\sqrt{5}}{8-\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{2\sqrt{2}-\sqrt{5}}{8-5}$$

3 olish uchun 8 dan 5 ni ayirish.

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