sqrt{1-(frac{7sqrt{5}}{27})^2} eching

$$\sqrt { 1 - ( \frac { 7 \sqrt { 5 } } { 27 } ) ^ { 2 } }$$

Baholash

$$\frac{22}{27}\approx 0,814814815$$

Yechim qadamlari

\frac{7\sqrt{5}}{27}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\sqrt{1-\frac{\left(7\sqrt{5}\right)^{2}}{27^{2}}}$$

\left(7\sqrt{5}\right)^{2} ni kengaytirish.

$$\sqrt{1-\frac{7^{2}\left(\sqrt{5}\right)^{2}}{27^{2}}}$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$\sqrt{1-\frac{49\left(\sqrt{5}\right)^{2}}{27^{2}}}$$

\sqrt{5} kvadrati – 5.

$$\sqrt{1-\frac{49\times 5}{27^{2}}}$$

245 hosil qilish uchun 49 va 5 ni ko'paytirish.

$$\sqrt{1-\frac{245}{27^{2}}}$$

2 daraja ko‘rsatkichini 27 ga hisoblang va 729 ni qiymatni oling.

$$\sqrt{1-\frac{245}{729}}$$

\frac{484}{729} olish uchun 1 dan \frac{245}{729} ni ayirish.

$$\sqrt{\frac{484}{729}}$$

\frac{484}{729} boʻlinmasining kvadrat ildizini \frac{\sqrt{484}}{\sqrt{729}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{22}{27}$$

Omil

$$\frac{2 \cdot 11}{3 ^ {3}} = 0,8148148148148148$$