Løs 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)]}}

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

Evaluer

$$\frac{3}{4}=0,75$$

Løsningsvejledning

Multiplicer \frac{3}{2} og \frac{3}{10} for at få \frac{9}{20}.

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

Subtraher \frac{1}{3} fra 2 for at få \frac{5}{3}.

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

Beregn \frac{5}{3} til potensen af 2, og få \frac{25}{9}.

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

Multiplicer \frac{3}{5} og \frac{25}{9} for at få \frac{5}{3}.

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

Subtraher \frac{5}{3} fra \frac{9}{5} for at få \frac{2}{15}.

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

Multiplicer \frac{2}{15} og \frac{3}{2} for at få \frac{1}{5}.

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

Tilføj \frac{9}{20} og \frac{1}{5} for at få \frac{13}{20}.

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

Tilføj \frac{3}{5} og 2 for at få \frac{13}{5}.

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

Divider \frac{13}{20} med \frac{13}{5} ved at multiplicere \frac{13}{20} med den reciprokke værdi af \frac{13}{5}.

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

Multiplicer \frac{13}{20} og \frac{5}{13} for at få \frac{1}{4}.

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

Tilføj \frac{1}{4} og 3 for at få \frac{13}{4}.

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

Multiplicer \frac{2}{13} og \frac{13}{4} for at få \frac{1}{2}.

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

Tilføj \frac{1}{6} og \frac{1}{2} for at få \frac{2}{3}.

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

Multiplicer \frac{2}{3} og \frac{2}{3} for at få \frac{4}{9}.

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

Divider \frac{1}{4} med \frac{4}{9} ved at multiplicere \frac{1}{4} med den reciprokke værdi af \frac{4}{9}.

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

Multiplicer \frac{1}{4} og \frac{9}{4} for at få \frac{9}{16}.

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

Omskriv kvadratroden af inddelings \frac{9}{16} som opdeling af kvadratiske rødder \frac{\sqrt{9}}{\sqrt{16}}. Tag kvadratroden af både tælleren og nævneren.

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

Faktoriser

$$\frac{3}{2 ^ {2}} = 0,75$$