[sqrt{1/9+frac{6/18}}{5-23/3}]^3= eching

$$[ \frac { \sqrt { \frac { 1 } { 9 } + \frac { 6 } { 18 } } } { 5 - \frac { 23 } { 3 } } ] ^ { 3 } =$$

Baholash

$$-\frac{1}{64}=-0,015625$$

Yechim qadamlari

\frac{6}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\left(\frac{\sqrt{\frac{1}{9}+\frac{1}{3}}}{5-\frac{23}{3}}\right)^{3}$$

\frac{4}{9} olish uchun \frac{1}{9} va \frac{1}{3}'ni qo'shing.

$$\left(\frac{\sqrt{\frac{4}{9}}}{5-\frac{23}{3}}\right)^{3}$$

\frac{4}{9} boʻlinmasining kvadrat ildizini \frac{\sqrt{4}}{\sqrt{9}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\left(\frac{\frac{2}{3}}{5-\frac{23}{3}}\right)^{3}$$

-\frac{8}{3} olish uchun 5 dan \frac{23}{3} ni ayirish.

$$\left(\frac{\frac{2}{3}}{-\frac{8}{3}}\right)^{3}$$

\frac{2}{3} ni -\frac{8}{3} ga bo'lish \frac{2}{3} ga k'paytirish -\frac{8}{3} ga qaytarish.

$$\left(\frac{2}{3}\left(-\frac{3}{8}\right)\right)^{3}$$

-\frac{1}{4} hosil qilish uchun \frac{2}{3} va -\frac{3}{8} ni ko'paytirish.

$$\left(-\frac{1}{4}\right)^{3}$$

3 daraja ko‘rsatkichini -\frac{1}{4} ga hisoblang va -\frac{1}{64} ni qiymatni oling.

$$-\frac{1}{64}$$

Omil

$$-\frac{1}{64} = -0,015625$$