Atrisiniet 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}}

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

Izrēķināt

$$\frac{13\sqrt{2009635}}{15}\approx 1228,600495596$$

Atrisinājuma darbības

Atņemiet 3998 no 396, lai iegūtu -3602.

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

Aprēķiniet -3602 pakāpē 2 un iegūstiet 12974404.

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

Atņemiet 3998 no 398, lai iegūtu -3600.

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

Aprēķiniet -3600 pakāpē 2 un iegūstiet 12960000.

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

Saskaitiet 12974404 un 12960000, lai iegūtu 25934404.

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

Atņemiet 3998 no 395, lai iegūtu -3603.

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

Aprēķiniet -3603 pakāpē 2 un iegūstiet 12981609.

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

Saskaitiet 25934404 un 12981609, lai iegūtu 38916013.

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

Atņemiet 3998 no 403, lai iegūtu -3595.

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

Aprēķiniet -3595 pakāpē 2 un iegūstiet 12924025.

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

Saskaitiet 38916013 un 12924025, lai iegūtu 51840038.

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

Atņemiet 3998 no 399, lai iegūtu -3599.

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

Aprēķiniet -3599 pakāpē 2 un iegūstiet 12952801.

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

Saskaitiet 51840038 un 12952801, lai iegūtu 64792839.

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

Atņemiet 3998 no 403, lai iegūtu -3595.

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

Aprēķiniet -3595 pakāpē 2 un iegūstiet 12924025.

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

Saskaitiet 64792839 un 12924025, lai iegūtu 77716864.

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

Atņemiet 3998 no 402, lai iegūtu -3596.

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

Aprēķiniet -3596 pakāpē 2 un iegūstiet 12931216.

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

Saskaitiet 77716864 un 12931216, lai iegūtu 90648080.

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

Atņemiet 3998 no 399, lai iegūtu -3599.

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

Aprēķiniet -3599 pakāpē 2 un iegūstiet 12952801.

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

Saskaitiet 90648080 un 12952801, lai iegūtu 103600881.

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

Atņemiet 3998 no 404, lai iegūtu -3594.

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

Aprēķiniet -3594 pakāpē 2 un iegūstiet 12916836.

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

Saskaitiet 103600881 un 12916836, lai iegūtu 116517717.

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

Saskaitiet 399 un 3998, lai iegūtu 4397.

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

Aprēķiniet 4397 pakāpē 2 un iegūstiet 19333609.

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

Saskaitiet 116517717 un 19333609, lai iegūtu 135851326.

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

Vienādot daļskaitli \frac{135851326}{90} līdz mazākajam loceklim, izvelkot un saīsinot 2.

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

Pārrakstiet dalījuma kvadrātsakni \sqrt{\frac{67925663}{45}} kā kvadrātveida saknes \frac{\sqrt{67925663}}{\sqrt{45}}.

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

Sadaliet reizinātājos 67925663=13^{2}\times 401927. Pārrakstiet reizinājuma kvadrātsakni \sqrt{13^{2}\times 401927} kā kvadrātveida saknes \sqrt{13^{2}}\sqrt{401927}. Izvelciet kvadrātsakni no 13^{2}.

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

Sadaliet reizinātājos 45=3^{2}\times 5. Pārrakstiet reizinājuma kvadrātsakni \sqrt{3^{2}\times 5} kā kvadrātveida saknes \sqrt{3^{2}}\sqrt{5}. Izvelciet kvadrātsakni no 3^{2}.

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

Atbrīvojieties no iracionalitātes saucēju ar \frac{13\sqrt{401927}}{3\sqrt{5}}, reizinot skaitītāju un saucēju ar \sqrt{5}.

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

Skaitļa \sqrt{5} kvadrāts ir 5.

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

Lai reiziniet \sqrt{401927} un \sqrt{5}, reiziniet numurus zem kvadrātveida saknes.

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

Reiziniet 3 un 5, lai iegūtu 15.

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