2sqrt{3}divsqrt{7/3}*sqrt{7/5} eching

$$2 \sqrt{ 3 } \div \sqrt{ \frac{ 7 }{ 3 } } \times \sqrt{ \frac{ 7 }{ 5 } }$$

Baholash

$$\frac{6\sqrt{5}}{5}\approx 2,683281573$$

Yechim qadamlari

\sqrt{\frac{7}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{7}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{7}{5}}$$

\frac{\sqrt{7}}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{7}{5}}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{7}{5}}$$

\sqrt{7} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{2\sqrt{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{7}{5}}$$

2\sqrt{3} ni \frac{\sqrt{21}}{3} ga bo'lish 2\sqrt{3} ga k'paytirish \frac{\sqrt{21}}{3} ga qaytarish.

$$\frac{2\sqrt{3}\times 3}{\sqrt{21}}\sqrt{\frac{7}{5}}$$

\frac{2\sqrt{3}\times 3}{\sqrt{21}} maxrajini \sqrt{21} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{7}{5}}$$

\sqrt{21} kvadrati – 21.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{6\sqrt{3}\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Faktor: 21=3\times 7. \sqrt{3\times 7} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{7} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{6\sqrt{3}\sqrt{3}\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$\frac{6\times 3\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$\frac{18\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

\frac{6}{7}\sqrt{7} ni olish uchun 18\sqrt{7} ni 21 ga bo‘ling.

$$\frac{6}{7}\sqrt{7}\sqrt{\frac{7}{5}}$$

\sqrt{\frac{7}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{7}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}}{\sqrt{5}}$$

\frac{\sqrt{7}}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

\sqrt{7} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{35}}{5}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{6}{7} ni \frac{\sqrt{35}}{5} ga ko‘paytiring.

$$\frac{6\sqrt{35}}{7\times 5}\sqrt{7}$$

35 hosil qilish uchun 7 va 5 ni ko'paytirish.

$$\frac{6\sqrt{35}}{35}\sqrt{7}$$

\frac{6\sqrt{35}}{35}\sqrt{7} ni yagona kasrga aylantiring.

$$\frac{6\sqrt{35}\sqrt{7}}{35}$$

Faktor: 35=7\times 5. \sqrt{7\times 5} koʻpaytmasining kvadrat ildizini \sqrt{7}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{6\sqrt{7}\sqrt{5}\sqrt{7}}{35}$$

7 hosil qilish uchun \sqrt{7} va \sqrt{7} ni ko'paytirish.

$$\frac{6\times 7\sqrt{5}}{35}$$

42 hosil qilish uchun 6 va 7 ni ko'paytirish.

$$\frac{42\sqrt{5}}{35}$$

\frac{6}{5}\sqrt{5} ni olish uchun 42\sqrt{5} ni 35 ga bo‘ling.

$$\frac{6}{5}\sqrt{5}$$