Issolvi 545/1520*560*sqrt{5222*20/2000}

$$\frac{ 545 }{ 1520 } \times 560 \times \sqrt{ \frac{ 5222 \times 20 }{ 2000 } }$$

Evalwa

$$\frac{763\sqrt{5222}}{38}\approx 1450.973147032$$

Passi tas-Soluzzjonijiet

Naqqas il-frazzjoni \frac{545}{1520} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$560\times \frac{109}{304}\sqrt{\frac{5222\times 20}{2000}}$$

Esprimi 560\times \frac{109}{304} bħala frazzjoni waħda.

$$\frac{560\times 109}{304}\sqrt{\frac{5222\times 20}{2000}}$$

Immultiplika 560 u 109 biex tikseb 61040.

$$\frac{61040}{304}\sqrt{\frac{5222\times 20}{2000}}$$

Naqqas il-frazzjoni \frac{61040}{304} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 16.

$$\frac{3815}{19}\sqrt{\frac{5222\times 20}{2000}}$$

Immultiplika 5222 u 20 biex tikseb 104440.

$$\frac{3815}{19}\sqrt{\frac{104440}{2000}}$$

Naqqas il-frazzjoni \frac{104440}{2000} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 40.

$$\frac{3815}{19}\sqrt{\frac{2611}{50}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{2611}{50}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{2611}}{\sqrt{50}}.

$$\frac{3815}{19}\times \frac{\sqrt{2611}}{\sqrt{50}}$$

Iffattura 50=5^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{3815}{19}\times \frac{\sqrt{2611}}{5\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2611}}{5\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{3815}{19}\times \frac{\sqrt{2611}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{3815}{19}\times \frac{\sqrt{2611}\sqrt{2}}{5\times 2}$$

Biex timmultiplika \sqrt{2611} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{3815}{19}\times \frac{\sqrt{5222}}{5\times 2}$$

Immultiplika 5 u 2 biex tikseb 10.

$$\frac{3815}{19}\times \frac{\sqrt{5222}}{10}$$

Immultiplika \frac{3815}{19} b'\frac{\sqrt{5222}}{10} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{3815\sqrt{5222}}{19\times 10}$$

Annulla 5 fin-numeratur u d-denominatur.

$$\frac{763\sqrt{5222}}{2\times 19}$$

Immultiplika 2 u 19 biex tikseb 38.

$$\frac{763\sqrt{5222}}{38}$$