sqrt{{[(3/5+1/10):7/20-(6/5+frac{7}{2}-frac{14}{5})]:frac{2}{3}-frac{1}{15}}:(frac{2}{3})^2} eching

$$\sqrt { \{ [ ( \frac { 3 } { 5 } + \frac { 1 } { 10 } ) : \frac { 7 } { 20 } - ( \frac { 6 } { 5 } + \frac { 7 } { 2 } - \frac { 14 } { 5 } ) ] : \frac { 2 } { 3 } - \frac { 1 } { 15 } \} : ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Baholash

$$\frac{\sqrt{3}}{4}\approx 0,433012702$$

Yechim qadamlari

5 va 10 ning eng kichik umumiy karralisi 10 ga teng. \frac{3}{5} va \frac{1}{10} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{\frac{\frac{6}{10}+\frac{1}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{6}{10} va \frac{1}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{\frac{\frac{\frac{6+1}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

7 olish uchun 6 va 1'ni qo'shing.

$$\sqrt{\frac{\frac{\frac{\frac{7}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{7}{10} ni \frac{7}{20} ga bo'lish \frac{7}{10} ga k'paytirish \frac{7}{20} ga qaytarish.

$$\sqrt{\frac{\frac{\frac{7}{10}\times \frac{20}{7}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{10} ni \frac{20}{7} ga ko‘paytiring.

$$\sqrt{\frac{\frac{\frac{7\times 20}{10\times 7}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Surat va maxrajdagi ikkala 7 ni qisqartiring.

$$\sqrt{\frac{\frac{\frac{20}{10}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

2 ni olish uchun 20 ni 10 ga bo‘ling.

$$\sqrt{\frac{\frac{2-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

5 va 2 ning eng kichik umumiy karralisi 10 ga teng. \frac{6}{5} va \frac{7}{2} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{2-\left(\frac{12}{10}+\frac{35}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{12}{10} va \frac{35}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{\frac{2-\left(\frac{12+35}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

47 olish uchun 12 va 35'ni qo'shing.

$$\sqrt{\frac{\frac{2-\left(\frac{47}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

10 va 5 ning eng kichik umumiy karralisi 10 ga teng. \frac{47}{10} va \frac{14}{5} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{2-\left(\frac{47}{10}-\frac{28}{10}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{47}{10} va \frac{28}{10} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{\frac{2-\frac{47-28}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

19 olish uchun 47 dan 28 ni ayirish.

$$\sqrt{\frac{\frac{2-\frac{19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

2 ni \frac{20}{10} kasrga o‘giring.

$$\sqrt{\frac{\frac{\frac{20}{10}-\frac{19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{20}{10} va \frac{19}{10} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{\frac{\frac{20-19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

1 olish uchun 20 dan 19 ni ayirish.

$$\sqrt{\frac{\frac{\frac{1}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{1}{10} ni \frac{2}{3} ga bo'lish \frac{1}{10} ga k'paytirish \frac{2}{3} ga qaytarish.

$$\sqrt{\frac{\frac{1}{10}\times \frac{3}{2}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{10} ni \frac{3}{2} ga ko‘paytiring.

$$\sqrt{\frac{\frac{1\times 3}{10\times 2}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{1\times 3}{10\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{\frac{3}{20}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

20 va 15 ning eng kichik umumiy karralisi 60 ga teng. \frac{3}{20} va \frac{1}{15} ni 60 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{9}{60}-\frac{4}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{9}{60} va \frac{4}{60} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{\frac{9-4}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

5 olish uchun 9 dan 4 ni ayirish.

$$\sqrt{\frac{\frac{5}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

\frac{5}{60} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{\frac{1}{12}}{\left(\frac{2}{3}\right)^{2}}}$$

2 daraja ko‘rsatkichini \frac{2}{3} ga hisoblang va \frac{4}{9} ni qiymatni oling.

$$\sqrt{\frac{\frac{1}{12}}{\frac{4}{9}}}$$

\frac{1}{12} ni \frac{4}{9} ga bo'lish \frac{1}{12} ga k'paytirish \frac{4}{9} ga qaytarish.

$$\sqrt{\frac{1}{12}\times \frac{9}{4}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{12} ni \frac{9}{4} ga ko‘paytiring.

$$\sqrt{\frac{1\times 9}{12\times 4}}$$

\frac{1\times 9}{12\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{9}{48}}$$

\frac{9}{48} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{3}{16}}$$

\sqrt{\frac{3}{16}} boʻlinmasining kvadrat ildizini \frac{\sqrt{3}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{3}}{\sqrt{16}}$$

16 ning kvadrat ildizini hisoblab, 4 natijaga ega bo‘ling.

$$\frac{\sqrt{3}}{4}$$