sqrt{3/2*(5/4-10/9)+1/16-(frac{1}{2}-frac{7}{18}):frac{16}{3}}= eching

$$\sqrt { \frac { 3 } { 2 } \cdot ( \frac { 5 } { 4 } - \frac { 10 } { 9 } ) + \frac { 1 } { 16 } - ( \frac { 1 } { 2 } - \frac { 7 } { 18 } ) : \frac { 16 } { 3 } } =$$

Baholash

$$\frac{1}{2}=0,5$$

Yechim qadamlari

4 va 9 ning eng kichik umumiy karralisi 36 ga teng. \frac{5}{4} va \frac{10}{9} ni 36 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{3}{2}\left(\frac{45}{36}-\frac{40}{36}\right)+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

\frac{45}{36} va \frac{40}{36} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{3}{2}\times \frac{45-40}{36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

5 olish uchun 45 dan 40 ni ayirish.

$$\sqrt{\frac{3}{2}\times \frac{5}{36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{2} ni \frac{5}{36} ga ko‘paytiring.

$$\sqrt{\frac{3\times 5}{2\times 36}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

\frac{3\times 5}{2\times 36} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{15}{72}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

\frac{15}{72} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{5}{24}+\frac{1}{16}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

24 va 16 ning eng kichik umumiy karralisi 48 ga teng. \frac{5}{24} va \frac{1}{16} ni 48 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{10}{48}+\frac{3}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

\frac{10}{48} va \frac{3}{48} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{10+3}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

13 olish uchun 10 va 3'ni qo'shing.

$$\sqrt{\frac{13}{48}-\frac{\frac{1}{2}-\frac{7}{18}}{\frac{16}{3}}}$$

2 va 18 ning eng kichik umumiy karralisi 18 ga teng. \frac{1}{2} va \frac{7}{18} ni 18 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{13}{48}-\frac{\frac{9}{18}-\frac{7}{18}}{\frac{16}{3}}}$$

\frac{9}{18} va \frac{7}{18} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{13}{48}-\frac{\frac{9-7}{18}}{\frac{16}{3}}}$$

2 olish uchun 9 dan 7 ni ayirish.

$$\sqrt{\frac{13}{48}-\frac{\frac{2}{18}}{\frac{16}{3}}}$$

\frac{2}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{13}{48}-\frac{\frac{1}{9}}{\frac{16}{3}}}$$

\frac{1}{9} ni \frac{16}{3} ga bo'lish \frac{1}{9} ga k'paytirish \frac{16}{3} ga qaytarish.

$$\sqrt{\frac{13}{48}-\frac{1}{9}\times \frac{3}{16}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{9} ni \frac{3}{16} ga ko‘paytiring.

$$\sqrt{\frac{13}{48}-\frac{1\times 3}{9\times 16}}$$

\frac{1\times 3}{9\times 16} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{13}{48}-\frac{3}{144}}$$

\frac{3}{144} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{13}{48}-\frac{1}{48}}$$

\frac{13}{48} va \frac{1}{48} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{13-1}{48}}$$

12 olish uchun 13 dan 1 ni ayirish.

$$\sqrt{\frac{12}{48}}$$

\frac{12}{48} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\frac{1}{4} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{4}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{1}{2}$$

Omil

$$\frac{1}{2} = 0,5$$