Issolvi 85.3-78.2/sqrt{frac{6.5{8}+6.3/8}}

$$\frac{ 85.3-78.2 }{ \sqrt{ \frac{ 6.5 }{ 8 } + \frac{ 6.3 }{ 8 } } }$$

Evalwa

$$\frac{71\sqrt{10}}{40}\approx 5.613042847$$

Passi tas-Soluzzjonijiet

Naqqas 78.2 minn 85.3 biex tikseb 7.1.

$$\frac{7.1}{\sqrt{\frac{6.5}{8}+\frac{6.3}{8}}}$$

Espandi \frac{6.5}{8} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

$$\frac{7.1}{\sqrt{\frac{65}{80}+\frac{6.3}{8}}}$$

Naqqas il-frazzjoni \frac{65}{80} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$\frac{7.1}{\sqrt{\frac{13}{16}+\frac{6.3}{8}}}$$

Espandi \frac{6.3}{8} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

$$\frac{7.1}{\sqrt{\frac{13}{16}+\frac{63}{80}}}$$

L-inqas multipli komuni ta' 16 u 80 huwa 80. Ikkonverti \frac{13}{16} u \frac{63}{80} fi frazzjonijiet bid-denominatur 80.

$$\frac{7.1}{\sqrt{\frac{65}{80}+\frac{63}{80}}}$$

Billi \frac{65}{80} u \frac{63}{80} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{7.1}{\sqrt{\frac{65+63}{80}}}$$

Żid 65 u 63 biex tikseb 128.

$$\frac{7.1}{\sqrt{\frac{128}{80}}}$$

Naqqas il-frazzjoni \frac{128}{80} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 16.

$$\frac{7.1}{\sqrt{\frac{8}{5}}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{8}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{7.1}{\frac{\sqrt{8}}{\sqrt{5}}}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{7.1}{\frac{2\sqrt{2}}{\sqrt{5}}}$$

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{2}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{7.1}{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{7.1}{\frac{2\sqrt{2}\sqrt{5}}{5}}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{7.1}{\frac{2\sqrt{10}}{5}}$$

Iddividi 7.1 b'\frac{2\sqrt{10}}{5} billi timmultiplika 7.1 bir-reċiproku ta' \frac{2\sqrt{10}}{5}.

$$\frac{7.1\times 5}{2\sqrt{10}}$$

Irrazzjonalizza d-denominatur tal-\frac{7.1\times 5}{2\sqrt{10}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{10}.

$$\frac{7.1\times 5\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$\frac{7.1\times 5\sqrt{10}}{2\times 10}$$

Immultiplika 7.1 u 5 biex tikseb 35.5.

$$\frac{35.5\sqrt{10}}{2\times 10}$$

Immultiplika 2 u 10 biex tikseb 20.

$$\frac{35.5\sqrt{10}}{20}$$

Iddividi 35.5\sqrt{10} b'20 biex tikseb1.775\sqrt{10}.

$$1.775\sqrt{10}$$