Réitigh sqrt{6*{5/13*[7/3*(1/3+2):(2+1/2):(frac{5}{6}+frac{3}{2})+(1-frac{1}{5})]-frac{1}{2}}*{frac{5}{9}*[(frac{2}{15}+frac{5}{3}):frac{5}{2}]}^2}

$$\sqrt { 6 \times \{ \frac { 5 } { 13 } \times [ \frac { 7 } { 3 } \times ( \frac { 1 } { 3 } + 2 ) : ( 2 + \frac { 1 } { 2 } ) : ( \frac { 5 } { 6 } + \frac { 3 } { 2 } ) + ( 1 - \frac { 1 } { 5 } ) ] - \frac { 1 } { 2 } \} \times \{ \frac { 5 } { 9 } \times [ ( \frac { 2 } { 15 } + \frac { 5 } { 3 } ) : \frac { 5 } { 2 } ] \} ^ { 2 } }$$

Luacháil

$$\frac{2}{5}=0.4$$

Céimeanna Réitigh

Suimigh \frac{1}{3} agus 2 chun \frac{7}{3} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{7}{3}\times \frac{7}{3}}{2+\frac{1}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Méadaigh \frac{7}{3} agus \frac{7}{3} chun \frac{49}{9} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{49}{9}}{2+\frac{1}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Suimigh 2 agus \frac{1}{2} chun \frac{5}{2} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{49}{9}}{\frac{5}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Roinn \frac{49}{9} faoi \frac{5}{2} trí \frac{49}{9} a mhéadú faoi dheilín \frac{5}{2}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{49}{9}\times \frac{2}{5}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Méadaigh \frac{49}{9} agus \frac{2}{5} chun \frac{98}{45} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{98}{45}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Suimigh \frac{5}{6} agus \frac{3}{2} chun \frac{7}{3} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{98}{45}}{\frac{7}{3}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Roinn \frac{98}{45} faoi \frac{7}{3} trí \frac{98}{45} a mhéadú faoi dheilín \frac{7}{3}.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{98}{45}\times \frac{3}{7}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Méadaigh \frac{98}{45} agus \frac{3}{7} chun \frac{14}{15} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{14}{15}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Suimigh \frac{14}{15} agus 1 chun \frac{29}{15} a fháil.

$$\sqrt{6\left(\frac{5}{13}\left(\frac{29}{15}-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Dealaigh \frac{1}{5} ó \frac{29}{15} chun \frac{26}{15} a fháil.

$$\sqrt{6\left(\frac{5}{13}\times \frac{26}{15}-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Méadaigh \frac{5}{13} agus \frac{26}{15} chun \frac{2}{3} a fháil.

$$\sqrt{6\left(\frac{2}{3}-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Dealaigh \frac{1}{2} ó \frac{2}{3} chun \frac{1}{6} a fháil.

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

Méadaigh 6 agus \frac{1}{6} chun 1 a fháil.

$$\sqrt{\left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}$$

Suimigh \frac{2}{15} agus \frac{5}{3} chun \frac{9}{5} a fháil.

$$\sqrt{\left(\frac{5}{9}\times \frac{\frac{9}{5}}{\frac{5}{2}}\right)^{2}}$$

Roinn \frac{9}{5} faoi \frac{5}{2} trí \frac{9}{5} a mhéadú faoi dheilín \frac{5}{2}.

$$\sqrt{\left(\frac{5}{9}\times \frac{9}{5}\times \frac{2}{5}\right)^{2}}$$

Méadaigh \frac{9}{5} agus \frac{2}{5} chun \frac{18}{25} a fháil.

$$\sqrt{\left(\frac{5}{9}\times \frac{18}{25}\right)^{2}}$$

Méadaigh \frac{5}{9} agus \frac{18}{25} chun \frac{2}{5} a fháil.

$$\sqrt{\left(\frac{2}{5}\right)^{2}}$$

Ríomh cumhacht \frac{2}{5} de 2 agus faigh \frac{4}{25}.

$$\sqrt{\frac{4}{25}}$$

Athscríobh fréamh cearnach na roinnte \frac{4}{25} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{4}}{\sqrt{25}}. Tóg fréamh chearnach an uimhreora agus an ainmneora.

$$\frac{2}{5}$$

Fachtóirigh

$$\frac{2}{5} = 0.4$$