545/1520*560*sqrt{5222*20/2000} eching

$$\frac{ 545 }{ 1520 } \times 560 \times \sqrt{ \frac{ 5222 \times 20 }{ 2000 } }$$

Baholash

$$\frac{763\sqrt{5222}}{38}\approx 1450,973147032$$

Yechim qadamlari

\frac{545}{1520} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$560\times \frac{109}{304}\sqrt{\frac{5222\times 20}{2000}}$$

560\times \frac{109}{304} ni yagona kasrga aylantiring.

$$\frac{560\times 109}{304}\sqrt{\frac{5222\times 20}{2000}}$$

61040 hosil qilish uchun 560 va 109 ni ko'paytirish.

$$\frac{61040}{304}\sqrt{\frac{5222\times 20}{2000}}$$

\frac{61040}{304} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3815}{19}\sqrt{\frac{5222\times 20}{2000}}$$

104440 hosil qilish uchun 5222 va 20 ni ko'paytirish.

$$\frac{3815}{19}\sqrt{\frac{104440}{2000}}$$

\frac{104440}{2000} ulushini 40 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3815}{19}\sqrt{\frac{2611}{50}}$$

\sqrt{\frac{2611}{50}} boʻlinmasining kvadrat ildizini \frac{\sqrt{2611}}{\sqrt{50}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{3815}{19}\times \frac{\sqrt{2611}}{\sqrt{50}}$$

Faktor: 50=5^{2}\times 2. \sqrt{5^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$\frac{3815}{19}\times \frac{\sqrt{2611}}{5\sqrt{2}}$$

\frac{\sqrt{2611}}{5\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{3815}{19}\times \frac{\sqrt{2611}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{3815}{19}\times \frac{\sqrt{2611}\sqrt{2}}{5\times 2}$$

\sqrt{2611} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{3815}{19}\times \frac{\sqrt{5222}}{5\times 2}$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\frac{3815}{19}\times \frac{\sqrt{5222}}{10}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3815}{19} ni \frac{\sqrt{5222}}{10} ga ko‘paytiring.

$$\frac{3815\sqrt{5222}}{19\times 10}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{763\sqrt{5222}}{2\times 19}$$

38 hosil qilish uchun 2 va 19 ni ko'paytirish.

$$\frac{763\sqrt{5222}}{38}$$