Issolvi sqrt{(11/4*8/11)^2:[(23/12-3/2):frac{5}{4}]^2}-sqrt{10+[(frac{1}{2})^2:frac{1}{2}+frac{12}{13}*(frac{5}{4}-frac{1}{6})]:frac{8}{3}}

$$\sqrt { ( \frac { 11 } { 4 } \times \frac { 8 } { 11 } ) ^ { 2 } : [ ( \frac { 23 } { 12 } - \frac { 3 } { 2 } ) : \frac { 5 } { 4 } ] ^ { 2 } } - \sqrt { 10 + [ ( \frac { 1 } { 2 } ) ^ { 2 } : \frac { 1 } { 2 } + \frac { 12 } { 13 } \times ( \frac { 5 } { 4 } - \frac { 1 } { 6 } ) ] : \frac { 8 } { 3 } }$$

Evalwa

$$\frac{11}{4}=2.75$$

Passi tas-Soluzzjonijiet

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur. Naqas 1 minn 2 biex tikseb 1.

$$\sqrt{\frac{\left(\frac{11}{4}\times \frac{8}{11}\right)^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Immultiplika \frac{11}{4} u \frac{8}{11} biex tikseb 2.

$$\sqrt{\frac{2^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\sqrt{\frac{4}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Naqqas \frac{3}{2} minn \frac{23}{12} biex tikseb \frac{5}{12}.

$$\sqrt{\frac{4}{\left(\frac{\frac{5}{12}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Iddividi \frac{5}{12} b'\frac{5}{4} billi timmultiplika \frac{5}{12} bir-reċiproku ta' \frac{5}{4}.

$$\sqrt{\frac{4}{\left(\frac{5}{12}\times \frac{4}{5}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Immultiplika \frac{5}{12} u \frac{4}{5} biex tikseb \frac{1}{3}.

$$\sqrt{\frac{4}{\left(\frac{1}{3}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Ikkalkula \frac{1}{3} bil-power ta' 2 u tikseb \frac{1}{9}.

$$\sqrt{\frac{4}{\frac{1}{9}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

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

$$\sqrt{4\times 9}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Immultiplika 4 u 9 biex tikseb 36.

$$\sqrt{36}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Ikkalkula l-għerq kwadrat ta' 36 u ikseb 6.

$$6-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Ikkalkula \frac{1}{2} bil-power ta' 1 u tikseb \frac{1}{2}.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Naqqas \frac{1}{6} minn \frac{5}{4} biex tikseb \frac{13}{12}.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\times \frac{13}{12}}{\frac{8}{3}}}$$

Immultiplika \frac{12}{13} u \frac{13}{12} biex tikseb 1.

$$6-\sqrt{10+\frac{\frac{1}{2}+1}{\frac{8}{3}}}$$

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

$$6-\sqrt{10+\frac{\frac{3}{2}}{\frac{8}{3}}}$$

Iddividi \frac{3}{2} b'\frac{8}{3} billi timmultiplika \frac{3}{2} bir-reċiproku ta' \frac{8}{3}.

$$6-\sqrt{10+\frac{3}{2}\times \frac{3}{8}}$$

Immultiplika \frac{3}{2} u \frac{3}{8} biex tikseb \frac{9}{16}.

$$6-\sqrt{10+\frac{9}{16}}$$

Żid 10 u \frac{9}{16} biex tikseb \frac{169}{16}.

$$6-\sqrt{\frac{169}{16}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \frac{169}{16} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{169}}{\sqrt{16}}. Ħu r-radiċi kwadrata tan-numeratur u d-denominatur.

$$6-\frac{13}{4}$$

Naqqas \frac{13}{4} minn 6 biex tikseb \frac{11}{4}.

$$\frac{11}{4}$$

Fattur

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2.75$$