1/2+1/4div1/3+(5/2)^2-sqrt{frac{81}{25}} eching

$$\frac { 1 } { 2 } + \frac { 1 } { 4 } \div \frac { 1 } { 3 } + ( \frac { 5 } { 2 } ) ^ { 2 } - \sqrt { \frac { 81 } { 25 } }$$

Baholash

$$\frac{57}{10}=5,7$$

Yechim qadamlari

\frac{1}{4} ni \frac{1}{3} ga bo'lish \frac{1}{4} ga k'paytirish \frac{1}{3} ga qaytarish.

$$\frac{1}{2}+\frac{1}{4}\times 3+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

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

$$\frac{1}{2}+\frac{3}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

2 va 4 ning eng kichik umumiy karralisi 4 ga teng. \frac{1}{2} va \frac{3}{4} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{4}+\frac{3}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

\frac{2}{4} va \frac{3}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2+3}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

5 olish uchun 2 va 3'ni qo'shing.

$$\frac{5}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

2 daraja ko‘rsatkichini \frac{5}{2} ga hisoblang va \frac{25}{4} ni qiymatni oling.

$$\frac{5}{4}+\frac{25}{4}-\sqrt{\frac{81}{25}}$$

\frac{5}{4} va \frac{25}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5+25}{4}-\sqrt{\frac{81}{25}}$$

30 olish uchun 5 va 25'ni qo'shing.

$$\frac{30}{4}-\sqrt{\frac{81}{25}}$$

\frac{30}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{15}{2}-\sqrt{\frac{81}{25}}$$

\frac{81}{25} boʻlinmasining kvadrat ildizini \frac{\sqrt{81}}{\sqrt{25}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{15}{2}-\frac{9}{5}$$

2 va 5 ning eng kichik umumiy karralisi 10 ga teng. \frac{15}{2} va \frac{9}{5} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\frac{75}{10}-\frac{18}{10}$$

\frac{75}{10} va \frac{18}{10} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{75-18}{10}$$

57 olish uchun 75 dan 18 ni ayirish.

$$\frac{57}{10}$$

Omil

$$\frac{3 \cdot 19}{2 \cdot 5} = 5\frac{7}{10} = 5,7$$