Issolvi sqrt{{[(3/5+1/10):7/20-(6/5+frac{7}{2}-frac{14}{5})]:frac{2}{3}-frac{1}{15}}:(frac{2}{3})^2}

$$\sqrt { \{ [ ( \frac { 3 } { 5 } + \frac { 1 } { 10 } ) : \frac { 7 } { 20 } - ( \frac { 6 } { 5 } + \frac { 7 } { 2 } - \frac { 14 } { 5 } ) ] : \frac { 2 } { 3 } - \frac { 1 } { 15 } \} : ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Evalwa

$$\frac{\sqrt{3}}{4}\approx 0.433012702$$

Passi tas-Soluzzjonijiet

L-inqas multipli komuni ta' 5 u 10 huwa 10. Ikkonverti \frac{3}{5} u \frac{1}{10} fi frazzjonijiet bid-denominatur 10.

$$\sqrt{\frac{\frac{\frac{\frac{6}{10}+\frac{1}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Billi \frac{6}{10} u \frac{1}{10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\sqrt{\frac{\frac{\frac{\frac{6+1}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Żid 6 u 1 biex tikseb 7.

$$\sqrt{\frac{\frac{\frac{\frac{7}{10}}{\frac{7}{20}}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Iddividi \frac{7}{10} b'\frac{7}{20} billi timmultiplika \frac{7}{10} bir-reċiproku ta' \frac{7}{20}.

$$\sqrt{\frac{\frac{\frac{7}{10}\times \frac{20}{7}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Immultiplika \frac{7}{10} b'\frac{20}{7} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\sqrt{\frac{\frac{\frac{7\times 20}{10\times 7}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Annulla 7 fin-numeratur u d-denominatur.

$$\sqrt{\frac{\frac{\frac{20}{10}-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Iddividi 20 b'10 biex tikseb2.

$$\sqrt{\frac{\frac{2-\left(\frac{6}{5}+\frac{7}{2}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

L-inqas multipli komuni ta' 5 u 2 huwa 10. Ikkonverti \frac{6}{5} u \frac{7}{2} fi frazzjonijiet bid-denominatur 10.

$$\sqrt{\frac{\frac{2-\left(\frac{12}{10}+\frac{35}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Billi \frac{12}{10} u \frac{35}{10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\sqrt{\frac{\frac{2-\left(\frac{12+35}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Żid 12 u 35 biex tikseb 47.

$$\sqrt{\frac{\frac{2-\left(\frac{47}{10}-\frac{14}{5}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

L-inqas multipli komuni ta' 10 u 5 huwa 10. Ikkonverti \frac{47}{10} u \frac{14}{5} fi frazzjonijiet bid-denominatur 10.

$$\sqrt{\frac{\frac{2-\left(\frac{47}{10}-\frac{28}{10}\right)}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Billi \frac{47}{10} u \frac{28}{10} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\sqrt{\frac{\frac{2-\frac{47-28}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Naqqas 28 minn 47 biex tikseb 19.

$$\sqrt{\frac{\frac{2-\frac{19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Ikkonverti 2 fi frazzjoni \frac{20}{10}.

$$\sqrt{\frac{\frac{\frac{20}{10}-\frac{19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Billi \frac{20}{10} u \frac{19}{10} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\sqrt{\frac{\frac{\frac{20-19}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Naqqas 19 minn 20 biex tikseb 1.

$$\sqrt{\frac{\frac{\frac{1}{10}}{\frac{2}{3}}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Iddividi \frac{1}{10} b'\frac{2}{3} billi timmultiplika \frac{1}{10} bir-reċiproku ta' \frac{2}{3}.

$$\sqrt{\frac{\frac{1}{10}\times \frac{3}{2}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Immultiplika \frac{1}{10} b'\frac{3}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\sqrt{\frac{\frac{1\times 3}{10\times 2}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{1\times 3}{10\times 2}.

$$\sqrt{\frac{\frac{3}{20}-\frac{1}{15}}{\left(\frac{2}{3}\right)^{2}}}$$

L-inqas multipli komuni ta' 20 u 15 huwa 60. Ikkonverti \frac{3}{20} u \frac{1}{15} fi frazzjonijiet bid-denominatur 60.

$$\sqrt{\frac{\frac{9}{60}-\frac{4}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

Billi \frac{9}{60} u \frac{4}{60} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\sqrt{\frac{\frac{9-4}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

Naqqas 4 minn 9 biex tikseb 5.

$$\sqrt{\frac{\frac{5}{60}}{\left(\frac{2}{3}\right)^{2}}}$$

Naqqas il-frazzjoni \frac{5}{60} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$\sqrt{\frac{\frac{1}{12}}{\left(\frac{2}{3}\right)^{2}}}$$

Ikkalkula \frac{2}{3} bil-power ta' 2 u tikseb \frac{4}{9}.

$$\sqrt{\frac{\frac{1}{12}}{\frac{4}{9}}}$$

Iddividi \frac{1}{12} b'\frac{4}{9} billi timmultiplika \frac{1}{12} bir-reċiproku ta' \frac{4}{9}.

$$\sqrt{\frac{1}{12}\times \frac{9}{4}}$$

Immultiplika \frac{1}{12} b'\frac{9}{4} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\sqrt{\frac{1\times 9}{12\times 4}}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{1\times 9}{12\times 4}.

$$\sqrt{\frac{9}{48}}$$

Naqqas il-frazzjoni \frac{9}{48} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\sqrt{\frac{3}{16}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{3}{16}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{3}}{\sqrt{16}}.

$$\frac{\sqrt{3}}{\sqrt{16}}$$

Ikkalkula l-għerq kwadrat ta' 16 u ikseb 4.

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