Réitigh sqrt{{3/2*3/10+[9/5-frac{3/5*(2-frac{1}{3})^2]*frac{3}{2}}:(frac{3}{5}+2)}{frac{2}{3}*[frac{1}{6}+frac{2}{13}*(frac{1}{4}+3)]}}

$$\sqrt { \frac { \{ \frac { 3 } { 2 } \times \frac { 3 } { 10 } + [ \frac { 9 } { 5 } - \frac { 3 } { 5 } \times ( 2 - \frac { 1 } { 3 } ) ^ { 2 } ] \times \frac { 3 } { 2 } \} : ( \frac { 3 } { 5 } + 2 ) } { \frac { 2 } { 3 } \times [ \frac { 1 } { 6 } + \frac { 2 } { 13 } \times ( \frac { 1 } { 4 } + 3 ) ] } }$$

Luacháil

$$\frac{3}{4}=0.75$$

Céimeanna Réitigh

Méadaigh \frac{3}{2} agus \frac{3}{10} chun \frac{9}{20} a fháil.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\left(2-\frac{1}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Dealaigh \frac{1}{3} ó 2 chun \frac{5}{3} a fháil.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \left(\frac{5}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Ríomh cumhacht \frac{5}{3} de 2 agus faigh \frac{25}{9}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \frac{25}{9}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Méadaigh \frac{3}{5} agus \frac{25}{9} chun \frac{5}{3} a fháil.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{5}{3}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Dealaigh \frac{5}{3} ó \frac{9}{5} chun \frac{2}{15} a fháil.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{2}{15}\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Méadaigh \frac{2}{15} agus \frac{3}{2} chun \frac{1}{5} a fháil.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{1}{5}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Suimigh \frac{9}{20} agus \frac{1}{5} chun \frac{13}{20} a fháil.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Suimigh \frac{3}{5} agus 2 chun \frac{13}{5} a fháil.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{13}{5}}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Roinn \frac{13}{20} faoi \frac{13}{5} trí \frac{13}{20} a mhéadú faoi dheilín \frac{13}{5}.

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

Méadaigh \frac{13}{20} agus \frac{5}{13} chun \frac{1}{4} a fháil.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Suimigh \frac{1}{4} agus 3 chun \frac{13}{4} a fháil.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\times \frac{13}{4}\right)}}$$

Méadaigh \frac{2}{13} agus \frac{13}{4} chun \frac{1}{2} a fháil.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{1}{2}\right)}}$$

Suimigh \frac{1}{6} agus \frac{1}{2} chun \frac{2}{3} a fháil.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\times \frac{2}{3}}}$$

Méadaigh \frac{2}{3} agus \frac{2}{3} chun \frac{4}{9} a fháil.

$$\sqrt{\frac{\frac{1}{4}}{\frac{4}{9}}}$$

Roinn \frac{1}{4} faoi \frac{4}{9} trí \frac{1}{4} a mhéadú faoi dheilín \frac{4}{9}.

$$\sqrt{\frac{1}{4}\times \frac{9}{4}}$$

Méadaigh \frac{1}{4} agus \frac{9}{4} chun \frac{9}{16} a fháil.

$$\sqrt{\frac{9}{16}}$$

Athscríobh fréamh cearnach na roinnte \frac{9}{16} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{9}}{\sqrt{16}}. Tóg fréamh chearnach an uimhreora agus an ainmneora.

$$\frac{3}{4}$$

Fachtóirigh

$$\frac{3}{2 ^ {2}} = 0.75$$