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}} eching

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

Baholash

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

Yechim qadamlari

-3602 olish uchun 396 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3602 ga hisoblang va 12974404 ni qiymatni oling.

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

-3600 olish uchun 398 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3600 ga hisoblang va 12960000 ni qiymatni oling.

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

25934404 olish uchun 12974404 va 12960000'ni qo'shing.

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

-3603 olish uchun 395 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3603 ga hisoblang va 12981609 ni qiymatni oling.

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

38916013 olish uchun 25934404 va 12981609'ni qo'shing.

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

-3595 olish uchun 403 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3595 ga hisoblang va 12924025 ni qiymatni oling.

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

51840038 olish uchun 38916013 va 12924025'ni qo'shing.

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

-3599 olish uchun 399 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3599 ga hisoblang va 12952801 ni qiymatni oling.

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

64792839 olish uchun 51840038 va 12952801'ni qo'shing.

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

-3595 olish uchun 403 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3595 ga hisoblang va 12924025 ni qiymatni oling.

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

77716864 olish uchun 64792839 va 12924025'ni qo'shing.

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

-3596 olish uchun 402 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3596 ga hisoblang va 12931216 ni qiymatni oling.

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

90648080 olish uchun 77716864 va 12931216'ni qo'shing.

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

-3599 olish uchun 399 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3599 ga hisoblang va 12952801 ni qiymatni oling.

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

103600881 olish uchun 90648080 va 12952801'ni qo'shing.

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

-3594 olish uchun 404 dan 3998 ni ayirish.

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

2 daraja ko‘rsatkichini -3594 ga hisoblang va 12916836 ni qiymatni oling.

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

116517717 olish uchun 103600881 va 12916836'ni qo'shing.

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

4397 olish uchun 399 va 3998'ni qo'shing.

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

2 daraja ko‘rsatkichini 4397 ga hisoblang va 19333609 ni qiymatni oling.

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

135851326 olish uchun 116517717 va 19333609'ni qo'shing.

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

\frac{135851326}{90} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\sqrt{\frac{67925663}{45}} boʻlinmasining kvadrat ildizini \frac{\sqrt{67925663}}{\sqrt{45}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

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

Faktor: 67925663=13^{2}\times 401927. \sqrt{13^{2}\times 401927} koʻpaytmasining kvadrat ildizini \sqrt{13^{2}}\sqrt{401927} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 13^{2} ning kvadrat ildizini chiqarish.

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

Faktor: 45=3^{2}\times 5. \sqrt{3^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

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

\frac{13\sqrt{401927}}{3\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{5} kvadrati – 5.

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

\sqrt{401927} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

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