sqrt{(5/3-3/5):[7/9-13/15:(frac{4}{5}+frac{1}{2})+frac{1}{3}]*frac{5}{3}}= eching

$$\sqrt { ( \frac { 5 } { 3 } - \frac { 3 } { 5 } ) : [ \frac { 7 } { 9 } - \frac { 13 } { 15 } : ( \frac { 4 } { 5 } + \frac { 1 } { 2 } ) + \frac { 1 } { 3 } ] \times \frac { 5 } { 3 } } =$$

Baholash

$$2$$

Yechim qadamlari

3 va 5 ning eng kichik umumiy karralisi 15 ga teng. \frac{5}{3} va \frac{3}{5} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{25}{15}-\frac{9}{15}}{\frac{7}{9}-\frac{\frac{13}{15}}{\frac{4}{5}+\frac{1}{2}}+\frac{1}{3}}\times \frac{5}{3}}$$

\frac{25}{15} va \frac{9}{15} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{\frac{25-9}{15}}{\frac{7}{9}-\frac{\frac{13}{15}}{\frac{4}{5}+\frac{1}{2}}+\frac{1}{3}}\times \frac{5}{3}}$$

16 olish uchun 25 dan 9 ni ayirish.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{\frac{13}{15}}{\frac{4}{5}+\frac{1}{2}}+\frac{1}{3}}\times \frac{5}{3}}$$

5 va 2 ning eng kichik umumiy karralisi 10 ga teng. \frac{4}{5} va \frac{1}{2} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{\frac{13}{15}}{\frac{8}{10}+\frac{5}{10}}+\frac{1}{3}}\times \frac{5}{3}}$$

\frac{8}{10} va \frac{5}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{\frac{13}{15}}{\frac{8+5}{10}}+\frac{1}{3}}\times \frac{5}{3}}$$

13 olish uchun 8 va 5'ni qo'shing.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}}\times \frac{5}{3}}$$

\frac{13}{15} ni \frac{13}{10} ga bo'lish \frac{13}{15} ga k'paytirish \frac{13}{10} ga qaytarish.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{13}{15}\times \frac{10}{13}+\frac{1}{3}}\times \frac{5}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{13}{15} ni \frac{10}{13} ga ko‘paytiring.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{13\times 10}{15\times 13}+\frac{1}{3}}\times \frac{5}{3}}$$

Surat va maxrajdagi ikkala 13 ni qisqartiring.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{10}{15}+\frac{1}{3}}\times \frac{5}{3}}$$

\frac{10}{15} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{2}{3}+\frac{1}{3}}\times \frac{5}{3}}$$

9 va 3 ning eng kichik umumiy karralisi 9 ga teng. \frac{7}{9} va \frac{2}{3} ni 9 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7}{9}-\frac{6}{9}+\frac{1}{3}}\times \frac{5}{3}}$$

\frac{7}{9} va \frac{6}{9} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{\frac{16}{15}}{\frac{7-6}{9}+\frac{1}{3}}\times \frac{5}{3}}$$

1 olish uchun 7 dan 6 ni ayirish.

$$\sqrt{\frac{\frac{16}{15}}{\frac{1}{9}+\frac{1}{3}}\times \frac{5}{3}}$$

9 va 3 ning eng kichik umumiy karralisi 9 ga teng. \frac{1}{9} va \frac{1}{3} ni 9 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{\frac{16}{15}}{\frac{1}{9}+\frac{3}{9}}\times \frac{5}{3}}$$

\frac{1}{9} va \frac{3}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{\frac{16}{15}}{\frac{1+3}{9}}\times \frac{5}{3}}$$

4 olish uchun 1 va 3'ni qo'shing.

$$\sqrt{\frac{\frac{16}{15}}{\frac{4}{9}}\times \frac{5}{3}}$$

\frac{16}{15} ni \frac{4}{9} ga bo'lish \frac{16}{15} ga k'paytirish \frac{4}{9} ga qaytarish.

$$\sqrt{\frac{16}{15}\times \frac{9}{4}\times \frac{5}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{16}{15} ni \frac{9}{4} ga ko‘paytiring.

$$\sqrt{\frac{16\times 9}{15\times 4}\times \frac{5}{3}}$$

\frac{16\times 9}{15\times 4} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{144}{60}\times \frac{5}{3}}$$

\frac{144}{60} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{12}{5}\times \frac{5}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{12}{5} ni \frac{5}{3} ga ko‘paytiring.

$$\sqrt{\frac{12\times 5}{5\times 3}}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\sqrt{\frac{12}{3}}$$

4 ni olish uchun 12 ni 3 ga bo‘ling.

$$\sqrt{4}$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$2$$

Omil

$$2$$