1000/sqrt{frac{500{72}+2500/2017div2}} eching

$$\frac{ 1000 }{ \sqrt{ \frac{ 500 }{ 72 } + \frac{ 2500 }{ 2017 \div 2 } } }$$

Baholash

$$\frac{120\sqrt{55205290}}{2737}\approx 325,759280011$$

Yechim qadamlari

\frac{500}{72} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{2500}{\frac{2017}{2}}}}$$

2500 ni \frac{2017}{2} ga bo'lish 2500 ga k'paytirish \frac{2017}{2} ga qaytarish.

$$\frac{1000}{\sqrt{\frac{125}{18}+2500\times \frac{2}{2017}}}$$

2500\times \frac{2}{2017} ni yagona kasrga aylantiring.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{2500\times 2}{2017}}}$$

5000 hosil qilish uchun 2500 va 2 ni ko'paytirish.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{5000}{2017}}}$$

18 va 2017 ning eng kichik umumiy karralisi 36306 ga teng. \frac{125}{18} va \frac{5000}{2017} ni 36306 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1000}{\sqrt{\frac{252125}{36306}+\frac{90000}{36306}}}$$

\frac{252125}{36306} va \frac{90000}{36306} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1000}{\sqrt{\frac{252125+90000}{36306}}}$$

342125 olish uchun 252125 va 90000'ni qo'shing.

$$\frac{1000}{\sqrt{\frac{342125}{36306}}}$$

\sqrt{\frac{342125}{36306}} boʻlinmasining kvadrat ildizini \frac{\sqrt{342125}}{\sqrt{36306}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{1000}{\frac{\sqrt{342125}}{\sqrt{36306}}}$$

Faktor: 342125=5^{2}\times 13685. \sqrt{5^{2}\times 13685} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{13685} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$\frac{1000}{\frac{5\sqrt{13685}}{\sqrt{36306}}}$$

Faktor: 36306=3^{2}\times 4034. \sqrt{3^{2}\times 4034} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{4034} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{1000}{\frac{5\sqrt{13685}}{3\sqrt{4034}}}$$

\frac{5\sqrt{13685}}{3\sqrt{4034}} maxrajini \sqrt{4034} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{1000}{\frac{5\sqrt{13685}\sqrt{4034}}{3\left(\sqrt{4034}\right)^{2}}}$$

\sqrt{4034} kvadrati – 4034.

$$\frac{1000}{\frac{5\sqrt{13685}\sqrt{4034}}{3\times 4034}}$$

\sqrt{13685} va \sqrt{4034} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{1000}{\frac{5\sqrt{55205290}}{3\times 4034}}$$

12102 hosil qilish uchun 3 va 4034 ni ko'paytirish.

$$\frac{1000}{\frac{5\sqrt{55205290}}{12102}}$$

1000 ni \frac{5\sqrt{55205290}}{12102} ga bo'lish 1000 ga k'paytirish \frac{5\sqrt{55205290}}{12102} ga qaytarish.

$$\frac{1000\times 12102}{5\sqrt{55205290}}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{200\times 12102}{\sqrt{55205290}}$$

\frac{200\times 12102}{\sqrt{55205290}} maxrajini \sqrt{55205290} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{200\times 12102\sqrt{55205290}}{\left(\sqrt{55205290}\right)^{2}}$$

\sqrt{55205290} kvadrati – 55205290.

$$\frac{200\times 12102\sqrt{55205290}}{55205290}$$

2420400 hosil qilish uchun 200 va 12102 ni ko'paytirish.

$$\frac{2420400\sqrt{55205290}}{55205290}$$

\frac{120}{2737}\sqrt{55205290} ni olish uchun 2420400\sqrt{55205290} ni 55205290 ga bo‘ling.

$$\frac{120}{2737}\sqrt{55205290}$$