Lutasin ang 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}}

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

I-evaluate

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

Mga Hakbang ng Solution

I-subtract ang 3998 mula sa 396 para makuha ang -3602.

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

Kalkulahin ang -3602 sa power ng 2 at kunin ang 12974404.

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

I-subtract ang 3998 mula sa 398 para makuha ang -3600.

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

Kalkulahin ang -3600 sa power ng 2 at kunin ang 12960000.

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

Idagdag ang 12974404 at 12960000 para makuha ang 25934404.

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

I-subtract ang 3998 mula sa 395 para makuha ang -3603.

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

Kalkulahin ang -3603 sa power ng 2 at kunin ang 12981609.

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

Idagdag ang 25934404 at 12981609 para makuha ang 38916013.

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

I-subtract ang 3998 mula sa 403 para makuha ang -3595.

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

Kalkulahin ang -3595 sa power ng 2 at kunin ang 12924025.

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

Idagdag ang 38916013 at 12924025 para makuha ang 51840038.

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

I-subtract ang 3998 mula sa 399 para makuha ang -3599.

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

Kalkulahin ang -3599 sa power ng 2 at kunin ang 12952801.

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

Idagdag ang 51840038 at 12952801 para makuha ang 64792839.

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

I-subtract ang 3998 mula sa 403 para makuha ang -3595.

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

Kalkulahin ang -3595 sa power ng 2 at kunin ang 12924025.

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

Idagdag ang 64792839 at 12924025 para makuha ang 77716864.

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

I-subtract ang 3998 mula sa 402 para makuha ang -3596.

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

Kalkulahin ang -3596 sa power ng 2 at kunin ang 12931216.

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

Idagdag ang 77716864 at 12931216 para makuha ang 90648080.

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

I-subtract ang 3998 mula sa 399 para makuha ang -3599.

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

Kalkulahin ang -3599 sa power ng 2 at kunin ang 12952801.

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

Idagdag ang 90648080 at 12952801 para makuha ang 103600881.

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

I-subtract ang 3998 mula sa 404 para makuha ang -3594.

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

Kalkulahin ang -3594 sa power ng 2 at kunin ang 12916836.

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

Idagdag ang 103600881 at 12916836 para makuha ang 116517717.

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

Idagdag ang 399 at 3998 para makuha ang 4397.

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

Kalkulahin ang 4397 sa power ng 2 at kunin ang 19333609.

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

Idagdag ang 116517717 at 19333609 para makuha ang 135851326.

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

Bawasan ang fraction \frac{135851326}{90} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 2.

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

I-rewrite ang square root ng division na \sqrt{\frac{67925663}{45}} bilang division ng mga square root na \frac{\sqrt{67925663}}{\sqrt{45}}.

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

I-factor out ang 67925663=13^{2}\times 401927. I-rewrite ang square root ng product na \sqrt{13^{2}\times 401927} bilang product ng mga square root na \sqrt{13^{2}}\sqrt{401927}. Kunin ang square root ng 13^{2}.

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

I-factor out ang 45=3^{2}\times 5. I-rewrite ang square root ng product na \sqrt{3^{2}\times 5} bilang product ng mga square root na \sqrt{3^{2}}\sqrt{5}. Kunin ang square root ng 3^{2}.

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

I-rationalize ang denominator ng \frac{13\sqrt{401927}}{3\sqrt{5}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{5}.

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

Ang square ng \sqrt{5} ay 5.

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

Para i-multiply ang \sqrt{401927} at \sqrt{5}, i-multiply ang mga numero sa ilalim ng square root.

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

I-multiply ang 3 at 5 para makuha ang 15.

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