sqrt{[4/13*(7-1/5*75/4)]:[16/3*(frac{4}{3}+frac{5}{6}:frac{1}{2})]}+sqrt{(frac{53}{5}-frac{63}{20}-5)*(1+frac{1}{4})} eching

$$\sqrt { [ \frac { 4 } { 13 } \times ( 7 - \frac { 1 } { 5 } \times \frac { 75 } { 4 } ) ] : [ \frac { 16 } { 3 } \times ( \frac { 4 } { 3 } + \frac { 5 } { 6 } : \frac { 1 } { 2 } ) ] } + \sqrt { ( \frac { 53 } { 5 } - \frac { 63 } { 20 } - 5 ) \times ( 1 + \frac { 1 } { 4 } ) }$$

Baholash

$$2$$

Yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{5} ni \frac{75}{4} ga ko‘paytiring.

$$\sqrt{\frac{\frac{4}{13}\left(7-\frac{1\times 75}{5\times 4}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{1\times 75}{5\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{\frac{4}{13}\left(7-\frac{75}{20}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{75}{20} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{\frac{4}{13}\left(7-\frac{15}{4}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

7 ni \frac{28}{4} kasrga o‘giring.

$$\sqrt{\frac{\frac{4}{13}\left(\frac{28}{4}-\frac{15}{4}\right)}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{28}{4} va \frac{15}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{\frac{4}{13}\times \frac{28-15}{4}}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

13 olish uchun 28 dan 15 ni ayirish.

$$\sqrt{\frac{\frac{4}{13}\times \frac{13}{4}}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{4}{13} va uning teskari kasrini \frac{13}{4} ni qisqartiring.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{\frac{5}{6}}{\frac{1}{2}}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{5}{6} ni \frac{1}{2} ga bo'lish \frac{5}{6} ga k'paytirish \frac{1}{2} ga qaytarish.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{5}{6}\times 2\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{5}{6}\times 2 ni yagona kasrga aylantiring.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{5\times 2}{6}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{10}{6}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{10}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{1}{\frac{16}{3}\left(\frac{4}{3}+\frac{5}{3}\right)}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{4}{3} va \frac{5}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{1}{\frac{16}{3}\times \frac{4+5}{3}}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

9 olish uchun 4 va 5'ni qo'shing.

$$\sqrt{\frac{1}{\frac{16}{3}\times \frac{9}{3}}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

3 ni olish uchun 9 ni 3 ga bo‘ling.

$$\sqrt{\frac{1}{\frac{16}{3}\times 3}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

3 va 3 ni qisqartiring.

$$\sqrt{\frac{1}{16}}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{1}{16} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{1}{4}+\sqrt{\left(\frac{53}{5}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

5 va 20 ning eng kichik umumiy karralisi 20 ga teng. \frac{53}{5} va \frac{63}{20} ni 20 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{4}+\sqrt{\left(\frac{212}{20}-\frac{63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

\frac{212}{20} va \frac{63}{20} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{4}+\sqrt{\left(\frac{212-63}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

149 olish uchun 212 dan 63 ni ayirish.

$$\frac{1}{4}+\sqrt{\left(\frac{149}{20}-5\right)\left(1+\frac{1}{4}\right)}$$

5 ni \frac{100}{20} kasrga o‘giring.

$$\frac{1}{4}+\sqrt{\left(\frac{149}{20}-\frac{100}{20}\right)\left(1+\frac{1}{4}\right)}$$

\frac{149}{20} va \frac{100}{20} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{4}+\sqrt{\frac{149-100}{20}\left(1+\frac{1}{4}\right)}$$

49 olish uchun 149 dan 100 ni ayirish.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\left(1+\frac{1}{4}\right)}$$

1 ni \frac{4}{4} kasrga o‘giring.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\left(\frac{4}{4}+\frac{1}{4}\right)}$$

\frac{4}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\times \frac{4+1}{4}}$$

5 olish uchun 4 va 1'ni qo'shing.

$$\frac{1}{4}+\sqrt{\frac{49}{20}\times \frac{5}{4}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{49}{20} ni \frac{5}{4} ga ko‘paytiring.

$$\frac{1}{4}+\sqrt{\frac{49\times 5}{20\times 4}}$$

\frac{49\times 5}{20\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1}{4}+\sqrt{\frac{245}{80}}$$

\frac{245}{80} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{4}+\sqrt{\frac{49}{16}}$$

\frac{49}{16} boʻlinmasining kvadrat ildizini \frac{\sqrt{49}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{1}{4}+\frac{7}{4}$$

\frac{1}{4} va \frac{7}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1+7}{4}$$

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

$$\frac{8}{4}$$

2 ni olish uchun 8 ni 4 ga bo‘ling.

$$2$$

Omil

$$2$$