sqrt{31/5}divsqrt{15/5} eching

$$\sqrt { 3 \frac { 1 } { 5 } } \div \sqrt { 1 \frac { 5 } { 5 } }$$

Baholash

$$\frac{2\sqrt{10}}{5}\approx 1,264911064$$

Yechim qadamlari

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

$$\frac{\sqrt{\frac{15+1}{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

16 olish uchun 15 va 1'ni qo'shing.

$$\frac{\sqrt{\frac{16}{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

\sqrt{\frac{16}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{16}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{\sqrt{16}}{\sqrt{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

16 ning kvadrat ildizini hisoblab, 4 natijaga ega bo‘ling.

$$\frac{\frac{4}{\sqrt{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

\frac{4}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{1\times 5+5}{5}}}$$

5 hosil qilish uchun 1 va 5 ni ko'paytirish.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{5+5}{5}}}$$

10 olish uchun 5 va 5'ni qo'shing.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{10}{5}}}$$

2 ni olish uchun 10 ni 5 ga bo‘ling.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{2}}$$

\frac{\frac{4\sqrt{5}}{5}}{\sqrt{2}} ni yagona kasrga aylantiring.

$$\frac{4\sqrt{5}}{5\sqrt{2}}$$

\frac{4\sqrt{5}}{5\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{4\sqrt{5}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{4\sqrt{5}\sqrt{2}}{5\times 2}$$

\sqrt{5} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{4\sqrt{10}}{5\times 2}$$

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

$$\frac{4\sqrt{10}}{10}$$

\frac{2}{5}\sqrt{10} ni olish uchun 4\sqrt{10} ni 10 ga bo‘ling.

$$\frac{2}{5}\sqrt{10}$$