Issolvi sqrt{frac{left(396-3998right)^2+left(398-3998right)^2+left(395-3998right)^2+left(403-3998right)^2+{left(399-3998right)}^{2}+{left(403-3998right)}^{2}+{left(402-3998right)}^2+{left(399-3998right)}^2+{left(404-3998right)}^2+{left(399+3998right)}^2}{90}}

$$\sqrt{ \frac{ { \left(396-3998 \right) }^{ 2 } + { \left(398-3998 \right) }^{ 2 } + { \left(395-3998 \right) }^{ 2 } + { \left(403-3998 \right) }^{ 2 } + { \left(399-3998 \right) }^{ 2 } + { \left(403-3998 \right) }^{ 2 } + { \left(402-3998 \right) }^{ 2 } + { \left(399-3998 \right) }^{ 2 } + { \left(404-3998 \right) }^{ 2 } + { \left(399+3998 \right) }^{ 2 } }{ 90 } }$$

Evalwa

$$\frac{13\sqrt{2009635}}{15}\approx 1228.600495596$$

Passi tas-Soluzzjonijiet

Naqqas 3998 minn 396 biex tikseb -3602.

$$\sqrt{\frac{\left(-3602\right)^{2}+\left(398-3998\right)^{2}+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3602 bil-power ta' 2 u tikseb 12974404.

$$\sqrt{\frac{12974404+\left(398-3998\right)^{2}+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 398 biex tikseb -3600.

$$\sqrt{\frac{12974404+\left(-3600\right)^{2}+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3600 bil-power ta' 2 u tikseb 12960000.

$$\sqrt{\frac{12974404+12960000+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 12974404 u 12960000 biex tikseb 25934404.

$$\sqrt{\frac{25934404+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 395 biex tikseb -3603.

$$\sqrt{\frac{25934404+\left(-3603\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3603 bil-power ta' 2 u tikseb 12981609.

$$\sqrt{\frac{25934404+12981609+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 25934404 u 12981609 biex tikseb 38916013.

$$\sqrt{\frac{38916013+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 403 biex tikseb -3595.

$$\sqrt{\frac{38916013+\left(-3595\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3595 bil-power ta' 2 u tikseb 12924025.

$$\sqrt{\frac{38916013+12924025+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 38916013 u 12924025 biex tikseb 51840038.

$$\sqrt{\frac{51840038+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 399 biex tikseb -3599.

$$\sqrt{\frac{51840038+\left(-3599\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3599 bil-power ta' 2 u tikseb 12952801.

$$\sqrt{\frac{51840038+12952801+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 51840038 u 12952801 biex tikseb 64792839.

$$\sqrt{\frac{64792839+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 403 biex tikseb -3595.

$$\sqrt{\frac{64792839+\left(-3595\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3595 bil-power ta' 2 u tikseb 12924025.

$$\sqrt{\frac{64792839+12924025+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 64792839 u 12924025 biex tikseb 77716864.

$$\sqrt{\frac{77716864+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 402 biex tikseb -3596.

$$\sqrt{\frac{77716864+\left(-3596\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3596 bil-power ta' 2 u tikseb 12931216.

$$\sqrt{\frac{77716864+12931216+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 77716864 u 12931216 biex tikseb 90648080.

$$\sqrt{\frac{90648080+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 399 biex tikseb -3599.

$$\sqrt{\frac{90648080+\left(-3599\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3599 bil-power ta' 2 u tikseb 12952801.

$$\sqrt{\frac{90648080+12952801+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Żid 90648080 u 12952801 biex tikseb 103600881.

$$\sqrt{\frac{103600881+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Naqqas 3998 minn 404 biex tikseb -3594.

$$\sqrt{\frac{103600881+\left(-3594\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Ikkalkula -3594 bil-power ta' 2 u tikseb 12916836.

$$\sqrt{\frac{103600881+12916836+\left(399+3998\right)^{2}}{90}}$$

Żid 103600881 u 12916836 biex tikseb 116517717.

$$\sqrt{\frac{116517717+\left(399+3998\right)^{2}}{90}}$$

Żid 399 u 3998 biex tikseb 4397.

$$\sqrt{\frac{116517717+4397^{2}}{90}}$$

Ikkalkula 4397 bil-power ta' 2 u tikseb 19333609.

$$\sqrt{\frac{116517717+19333609}{90}}$$

Żid 116517717 u 19333609 biex tikseb 135851326.

$$\sqrt{\frac{135851326}{90}}$$

Naqqas il-frazzjoni \frac{135851326}{90} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\sqrt{\frac{67925663}{45}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{67925663}{45}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{67925663}}{\sqrt{45}}.

$$\frac{\sqrt{67925663}}{\sqrt{45}}$$

Iffattura 67925663=13^{2}\times 401927. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{13^{2}\times 401927} bħala l-prodott tal-għeruq kwadrati \sqrt{13^{2}}\sqrt{401927}. Ħu l-għerq kwadrat ta' 13^{2}.

$$\frac{13\sqrt{401927}}{\sqrt{45}}$$

Iffattura 45=3^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{13\sqrt{401927}}{3\sqrt{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{13\sqrt{401927}}{3\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{13\sqrt{401927}\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{13\sqrt{401927}\sqrt{5}}{3\times 5}$$

Biex timmultiplika \sqrt{401927} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{13\sqrt{2009635}}{3\times 5}$$

Immultiplika 3 u 5 biex tikseb 15.

$$\frac{13\sqrt{2009635}}{15}$$