Issolvi 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)]}}

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

Evalwa

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

Passi tas-Soluzzjonijiet

Immultiplika \frac{3}{2} u \frac{3}{10} biex tikseb \frac{9}{20}.

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

Naqqas \frac{1}{3} minn 2 biex tikseb \frac{5}{3}.

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

Ikkalkula \frac{5}{3} bil-power ta' 2 u tikseb \frac{25}{9}.

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

Immultiplika \frac{3}{5} u \frac{25}{9} biex tikseb \frac{5}{3}.

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

Naqqas \frac{5}{3} minn \frac{9}{5} biex tikseb \frac{2}{15}.

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

Immultiplika \frac{2}{15} u \frac{3}{2} biex tikseb \frac{1}{5}.

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

Żid \frac{9}{20} u \frac{1}{5} biex tikseb \frac{13}{20}.

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

Żid \frac{3}{5} u 2 biex tikseb \frac{13}{5}.

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

Iddividi \frac{13}{20} b'\frac{13}{5} billi timmultiplika \frac{13}{20} bir-reċiproku ta' \frac{13}{5}.

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

Immultiplika \frac{13}{20} u \frac{5}{13} biex tikseb \frac{1}{4}.

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

Żid \frac{1}{4} u 3 biex tikseb \frac{13}{4}.

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

Immultiplika \frac{2}{13} u \frac{13}{4} biex tikseb \frac{1}{2}.

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

Żid \frac{1}{6} u \frac{1}{2} biex tikseb \frac{2}{3}.

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

Immultiplika \frac{2}{3} u \frac{2}{3} biex tikseb \frac{4}{9}.

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

Iddividi \frac{1}{4} b'\frac{4}{9} billi timmultiplika \frac{1}{4} bir-reċiproku ta' \frac{4}{9}.

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

Immultiplika \frac{1}{4} u \frac{9}{4} biex tikseb \frac{9}{16}.

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

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \frac{9}{16} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{9}}{\sqrt{16}}. Ħu r-radiċi kwadrata tan-numeratur u d-denominatur.

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

Fattur

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