Atrisiniet 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}}

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

Izrēķināt

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

Atrisinājuma darbības

Lai dalītu vienas bāzes pakāpes, atņemiet saucēja kāpinātāju no skaitītāja kāpinātāja. Lai iegūtu 1, no 2 atņemiet 1.

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

Reiziniet \frac{11}{4} un \frac{8}{11}, lai iegūtu 2.

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

Aprēķiniet 2 pakāpē 2 un iegūstiet 4.

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

Atņemiet \frac{3}{2} no \frac{23}{12}, lai iegūtu \frac{5}{12}.

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

Daliet \frac{5}{12} ar \frac{5}{4}, reizinot \frac{5}{12} ar apgriezto daļskaitli \frac{5}{4} .

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

Reiziniet \frac{5}{12} un \frac{4}{5}, lai iegūtu \frac{1}{3}.

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

Aprēķiniet \frac{1}{3} pakāpē 2 un iegūstiet \frac{1}{9}.

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

Daliet 4 ar \frac{1}{9}, reizinot 4 ar apgriezto daļskaitli \frac{1}{9} .

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

Reiziniet 4 un 9, lai iegūtu 36.

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

Aprēķināt kvadrātsakni no 36 un iegūt 6.

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

Aprēķiniet \frac{1}{2} pakāpē 1 un iegūstiet \frac{1}{2}.

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

Atņemiet \frac{1}{6} no \frac{5}{4}, lai iegūtu \frac{13}{12}.

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

Reiziniet \frac{12}{13} un \frac{13}{12}, lai iegūtu 1.

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

Saskaitiet \frac{1}{2} un 1, lai iegūtu \frac{3}{2}.

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

Daliet \frac{3}{2} ar \frac{8}{3}, reizinot \frac{3}{2} ar apgriezto daļskaitli \frac{8}{3} .

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

Reiziniet \frac{3}{2} un \frac{3}{8}, lai iegūtu \frac{9}{16}.

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

Saskaitiet 10 un \frac{9}{16}, lai iegūtu \frac{169}{16}.

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

Pārrakstiet dalījuma kvadrātsakni \frac{169}{16} kā kvadrātveida saknes \frac{\sqrt{169}}{\sqrt{16}}. Izrēķiniet gan skaitītāja, gan saucēja kvadrātsakni.

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

Atņemiet \frac{13}{4} no 6, lai iegūtu \frac{11}{4}.

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

Sadalīt reizinātājos

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