sqrt{(11/4*8/11)^2:[(23/12-3/2):frac{5}{4}]^2}-sqrt{10+[(frac{1}{2})^2:frac{1}{2}+frac{12}{13}*(frac{5}{4}-frac{1}{6})]:frac{8}{3}} eching

$$\sqrt { ( \frac { 11 } { 4 } \times \frac { 8 } { 11 } ) ^ { 2 } : [ ( \frac { 23 } { 12 } - \frac { 3 } { 2 } ) : \frac { 5 } { 4 } ] ^ { 2 } } - \sqrt { 10 + [ ( \frac { 1 } { 2 } ) ^ { 2 } : \frac { 1 } { 2 } + \frac { 12 } { 13 } \times ( \frac { 5 } { 4 } - \frac { 1 } { 6 } ) ] : \frac { 8 } { 3 } }$$

Baholash

$$\frac{11}{4}=2,75$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 2 dan 1 ni ayirib, 1 ni oling.

$$\sqrt{\frac{\left(\frac{11}{4}\times \frac{8}{11}\right)^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

2 hosil qilish uchun \frac{11}{4} va \frac{8}{11} ni ko'paytirish.

$$\sqrt{\frac{2^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\sqrt{\frac{4}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

\frac{5}{12} olish uchun \frac{23}{12} dan \frac{3}{2} ni ayirish.

$$\sqrt{\frac{4}{\left(\frac{\frac{5}{12}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

\frac{5}{12} ni \frac{5}{4} ga bo'lish \frac{5}{12} ga k'paytirish \frac{5}{4} ga qaytarish.

$$\sqrt{\frac{4}{\left(\frac{5}{12}\times \frac{4}{5}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

\frac{1}{3} hosil qilish uchun \frac{5}{12} va \frac{4}{5} ni ko'paytirish.

$$\sqrt{\frac{4}{\left(\frac{1}{3}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

2 daraja ko‘rsatkichini \frac{1}{3} ga hisoblang va \frac{1}{9} ni qiymatni oling.

$$\sqrt{\frac{4}{\frac{1}{9}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

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

$$\sqrt{4\times 9}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

36 hosil qilish uchun 4 va 9 ni ko'paytirish.

$$\sqrt{36}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

36 ning kvadrat ildizini hisoblab, 6 natijaga ega bo‘ling.

$$6-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

1 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{2} ni qiymatni oling.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

\frac{13}{12} olish uchun \frac{5}{4} dan \frac{1}{6} ni ayirish.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\times \frac{13}{12}}{\frac{8}{3}}}$$

1 hosil qilish uchun \frac{12}{13} va \frac{13}{12} ni ko'paytirish.

$$6-\sqrt{10+\frac{\frac{1}{2}+1}{\frac{8}{3}}}$$

\frac{3}{2} olish uchun \frac{1}{2} va 1'ni qo'shing.

$$6-\sqrt{10+\frac{\frac{3}{2}}{\frac{8}{3}}}$$

\frac{3}{2} ni \frac{8}{3} ga bo'lish \frac{3}{2} ga k'paytirish \frac{8}{3} ga qaytarish.

$$6-\sqrt{10+\frac{3}{2}\times \frac{3}{8}}$$

\frac{9}{16} hosil qilish uchun \frac{3}{2} va \frac{3}{8} ni ko'paytirish.

$$6-\sqrt{10+\frac{9}{16}}$$

\frac{169}{16} olish uchun 10 va \frac{9}{16}'ni qo'shing.

$$6-\sqrt{\frac{169}{16}}$$

\frac{169}{16} boʻlinmasining kvadrat ildizini \frac{\sqrt{169}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$6-\frac{13}{4}$$

\frac{11}{4} olish uchun 6 dan \frac{13}{4} ni ayirish.

$$\frac{11}{4}$$

Omil

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2,75$$