sqrt{[(3/4-7/4*1/4)*8/5+(1+frac{3}{8}:frac{1}{4})*frac{3}{10}]*frac{1}{4}+frac{5}{4}} eching

$$\sqrt { [ ( \frac { 3 } { 4 } - \frac { 7 } { 4 } \times \frac { 1 } { 4 } ) \times \frac { 8 } { 5 } + ( 1 + \frac { 3 } { 8 } : \frac { 1 } { 4 } ) \times \frac { 3 } { 10 } ] \times \frac { 1 } { 4 } + \frac { 5 } { 4 } }$$

Baholash

$$\frac{5}{4}=1,25$$

Yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{4} ni \frac{1}{4} ga ko‘paytiring.

$$\sqrt{\left(\left(\frac{3}{4}-\frac{7\times 1}{4\times 4}\right)\times \frac{8}{5}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{7\times 1}{4\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\left(\left(\frac{3}{4}-\frac{7}{16}\right)\times \frac{8}{5}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

4 va 16 ning eng kichik umumiy karralisi 16 ga teng. \frac{3}{4} va \frac{7}{16} ni 16 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\left(\left(\frac{12}{16}-\frac{7}{16}\right)\times \frac{8}{5}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{12}{16} va \frac{7}{16} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\left(\frac{12-7}{16}\times \frac{8}{5}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

5 olish uchun 12 dan 7 ni ayirish.

$$\sqrt{\left(\frac{5}{16}\times \frac{8}{5}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{16} ni \frac{8}{5} ga ko‘paytiring.

$$\sqrt{\left(\frac{5\times 8}{16\times 5}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\sqrt{\left(\frac{8}{16}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{8}{16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{1}{2}+\left(1+\frac{\frac{3}{8}}{\frac{1}{4}}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{3}{8} ni \frac{1}{4} ga bo'lish \frac{3}{8} ga k'paytirish \frac{1}{4} ga qaytarish.

$$\sqrt{\left(\frac{1}{2}+\left(1+\frac{3}{8}\times 4\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{3}{8}\times 4 ni yagona kasrga aylantiring.

$$\sqrt{\left(\frac{1}{2}+\left(1+\frac{3\times 4}{8}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$\sqrt{\left(\frac{1}{2}+\left(1+\frac{12}{8}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\left(\frac{1}{2}+\left(1+\frac{3}{2}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

1 ni \frac{2}{2} kasrga o‘giring.

$$\sqrt{\left(\frac{1}{2}+\left(\frac{2}{2}+\frac{3}{2}\right)\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

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

$$\sqrt{\left(\frac{1}{2}+\frac{2+3}{2}\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

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

$$\sqrt{\left(\frac{1}{2}+\frac{5}{2}\times \frac{3}{10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{2} ni \frac{3}{10} ga ko‘paytiring.

$$\sqrt{\left(\frac{1}{2}+\frac{5\times 3}{2\times 10}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{5\times 3}{2\times 10} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\left(\frac{1}{2}+\frac{15}{20}\right)\times \frac{1}{4}+\frac{5}{4}}$$

\frac{15}{20} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

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.

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

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

$$\sqrt{\frac{2+3}{4}\times \frac{1}{4}+\frac{5}{4}}$$

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

$$\sqrt{\frac{5}{4}\times \frac{1}{4}+\frac{5}{4}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{4} ni \frac{1}{4} ga ko‘paytiring.

$$\sqrt{\frac{5\times 1}{4\times 4}+\frac{5}{4}}$$

\frac{5\times 1}{4\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{5}{16}+\frac{5}{4}}$$

16 va 4 ning eng kichik umumiy karralisi 16 ga teng. \frac{5}{16} va \frac{5}{4} ni 16 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{5}{16}+\frac{20}{16}}$$

\frac{5}{16} va \frac{20}{16} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{5+20}{16}}$$

25 olish uchun 5 va 20'ni qo'shing.

$$\sqrt{\frac{25}{16}}$$

\frac{25}{16} boʻlinmasining kvadrat ildizini \frac{\sqrt{25}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{5}{4}$$

Omil

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1,25$$