sqrt{5/7}*sqrt[3]{343/125}= eching

$$\sqrt { \frac { 5 } { 7 } } \times \sqrt[ 3 ] { \frac { 343 } { 125 } } =$$

Baholash

$$\frac{\sqrt{35}}{5}\approx 1,183215957$$

Yechim qadamlari

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

$$\frac{\sqrt{5}}{\sqrt{7}}\sqrt[3]{\frac{343}{125}}$$

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

$$\frac{\sqrt{5}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\sqrt[3]{\frac{343}{125}}$$

\sqrt{7} kvadrati – 7.

$$\frac{\sqrt{5}\sqrt{7}}{7}\sqrt[3]{\frac{343}{125}}$$

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

$$\frac{\sqrt{35}}{7}\sqrt[3]{\frac{343}{125}}$$

\sqrt[3]{\frac{343}{125}} ni hisoblab, \frac{7}{5} natijasiga ega bo‘ling.

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

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

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

Surat va maxrajdagi ikkala 7 ni qisqartiring.

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