{left(5sqrt{5/9}right)}^2 eching

$${ \left(5 \sqrt{ \frac{ 5 }{ 9 } } \right) }^{ 2 }$$

Baholash

$$\frac{125}{9}\approx 13,888888889$$

Yechim qadamlari

\sqrt{\frac{5}{9}} boʻlinmasining kvadrat ildizini \frac{\sqrt{5}}{\sqrt{9}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\left(5\times \frac{\sqrt{5}}{\sqrt{9}}\right)^{2}$$

9 ning kvadrat ildizini hisoblab, 3 natijaga ega bo‘ling.

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

5\times \frac{\sqrt{5}}{3} ni yagona kasrga aylantiring.

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

\frac{5\sqrt{5}}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{25\left(\sqrt{5}\right)^{2}}{3^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{25\times 5}{3^{2}}$$

125 hosil qilish uchun 25 va 5 ni ko'paytirish.

$$\frac{125}{3^{2}}$$

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

$$\frac{125}{9}$$

Omil

$$\frac{5 ^ {3}}{3 ^ {2}} = 13\frac{8}{9} = 13,88888888888889$$