Issolvi 1000/sqrt{frac{500{72}+2500/2017div2}}

$$\frac{ 1000 }{ \sqrt{ \frac{ 500 }{ 72 } + \frac{ 2500 }{ 2017 \div 2 } } }$$

Evalwa

$$\frac{120\sqrt{55205290}}{2737}\approx 325.759280011$$

Passi tas-Soluzzjonijiet

Naqqas il-frazzjoni \frac{500}{72} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 4.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{2500}{\frac{2017}{2}}}}$$

Iddividi 2500 b'\frac{2017}{2} billi timmultiplika 2500 bir-reċiproku ta' \frac{2017}{2}.

$$\frac{1000}{\sqrt{\frac{125}{18}+2500\times \frac{2}{2017}}}$$

Esprimi 2500\times \frac{2}{2017} bħala frazzjoni waħda.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{2500\times 2}{2017}}}$$

Immultiplika 2500 u 2 biex tikseb 5000.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{5000}{2017}}}$$

L-inqas multipli komuni ta' 18 u 2017 huwa 36306. Ikkonverti \frac{125}{18} u \frac{5000}{2017} fi frazzjonijiet bid-denominatur 36306.

$$\frac{1000}{\sqrt{\frac{252125}{36306}+\frac{90000}{36306}}}$$

Billi \frac{252125}{36306} u \frac{90000}{36306} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{1000}{\sqrt{\frac{252125+90000}{36306}}}$$

Żid 252125 u 90000 biex tikseb 342125.

$$\frac{1000}{\sqrt{\frac{342125}{36306}}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{342125}{36306}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{342125}}{\sqrt{36306}}.

$$\frac{1000}{\frac{\sqrt{342125}}{\sqrt{36306}}}$$

Iffattura 342125=5^{2}\times 13685. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 13685} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{13685}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{1000}{\frac{5\sqrt{13685}}{\sqrt{36306}}}$$

Iffattura 36306=3^{2}\times 4034. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 4034} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{4034}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{1000}{\frac{5\sqrt{13685}}{3\sqrt{4034}}}$$

Irrazzjonalizza d-denominatur tal-\frac{5\sqrt{13685}}{3\sqrt{4034}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{4034}.

$$\frac{1000}{\frac{5\sqrt{13685}\sqrt{4034}}{3\left(\sqrt{4034}\right)^{2}}}$$

Il-kwadrat ta' \sqrt{4034} huwa 4034.

$$\frac{1000}{\frac{5\sqrt{13685}\sqrt{4034}}{3\times 4034}}$$

Biex timmultiplika \sqrt{13685} u \sqrt{4034}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{1000}{\frac{5\sqrt{55205290}}{3\times 4034}}$$

Immultiplika 3 u 4034 biex tikseb 12102.

$$\frac{1000}{\frac{5\sqrt{55205290}}{12102}}$$

Iddividi 1000 b'\frac{5\sqrt{55205290}}{12102} billi timmultiplika 1000 bir-reċiproku ta' \frac{5\sqrt{55205290}}{12102}.

$$\frac{1000\times 12102}{5\sqrt{55205290}}$$

Annulla 5 fin-numeratur u d-denominatur.

$$\frac{200\times 12102}{\sqrt{55205290}}$$

Irrazzjonalizza d-denominatur tal-\frac{200\times 12102}{\sqrt{55205290}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{55205290}.

$$\frac{200\times 12102\sqrt{55205290}}{\left(\sqrt{55205290}\right)^{2}}$$

Il-kwadrat ta' \sqrt{55205290} huwa 55205290.

$$\frac{200\times 12102\sqrt{55205290}}{55205290}$$

Immultiplika 200 u 12102 biex tikseb 2420400.

$$\frac{2420400\sqrt{55205290}}{55205290}$$

Iddividi 2420400\sqrt{55205290} b'55205290 biex tikseb\frac{120}{2737}\sqrt{55205290}.

$$\frac{120}{2737}\sqrt{55205290}$$