Lutasin ang 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}

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

I-evaluate

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

Mga Hakbang ng Solution

Idagdag ang \frac{1}{3} at 2 para makuha ang \frac{7}{3}.

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

I-multiply ang \frac{7}{3} at \frac{7}{3} para makuha ang \frac{49}{9}.

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

Idagdag ang 2 at \frac{1}{2} para makuha ang \frac{5}{2}.

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

I-divide ang \frac{49}{9} gamit ang \frac{5}{2} sa pamamagitan ng pagmu-multiply sa \frac{49}{9} gamit ang reciprocal ng \frac{5}{2}.

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

I-multiply ang \frac{49}{9} at \frac{2}{5} para makuha ang \frac{98}{45}.

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

Idagdag ang \frac{5}{6} at \frac{3}{2} para makuha ang \frac{7}{3}.

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

I-divide ang \frac{98}{45} gamit ang \frac{7}{3} sa pamamagitan ng pagmu-multiply sa \frac{98}{45} gamit ang reciprocal ng \frac{7}{3}.

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

I-multiply ang \frac{98}{45} at \frac{3}{7} para makuha ang \frac{14}{15}.

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

Idagdag ang \frac{14}{15} at 1 para makuha ang \frac{29}{15}.

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

I-subtract ang \frac{1}{5} mula sa \frac{29}{15} para makuha ang \frac{26}{15}.

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

I-multiply ang \frac{5}{13} at \frac{26}{15} para makuha ang \frac{2}{3}.

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

I-subtract ang \frac{1}{2} mula sa \frac{2}{3} para makuha ang \frac{1}{6}.

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

I-multiply ang 6 at \frac{1}{6} para makuha ang 1.

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

Idagdag ang \frac{2}{15} at \frac{5}{3} para makuha ang \frac{9}{5}.

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

I-divide ang \frac{9}{5} gamit ang \frac{5}{2} sa pamamagitan ng pagmu-multiply sa \frac{9}{5} gamit ang reciprocal ng \frac{5}{2}.

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

I-multiply ang \frac{9}{5} at \frac{2}{5} para makuha ang \frac{18}{25}.

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

I-multiply ang \frac{5}{9} at \frac{18}{25} para makuha ang \frac{2}{5}.

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

Kalkulahin ang \frac{2}{5} sa power ng 2 at kunin ang \frac{4}{25}.

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

I-rewrite ang square root ng division na \frac{4}{25} bilang division ng mga square root na \frac{\sqrt{4}}{\sqrt{25}}. Kunin ang square root ng numerator at denominator.

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

I-factor

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