2sqrt{2}*5sqrt{1/6} eching

$$2 \sqrt{ 2 } \times 5 \sqrt{ \frac{ 1 }{ 6 } }$$

Baholash

$$\frac{10\sqrt{3}}{3}\approx 5,773502692$$

Yechim qadamlari

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

$$10\sqrt{2}\sqrt{\frac{1}{6}}$$

\sqrt{\frac{1}{6}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{6}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$10\sqrt{2}\times \frac{\sqrt{1}}{\sqrt{6}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$10\sqrt{2}\times \frac{1}{\sqrt{6}}$$

\frac{1}{\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$10\sqrt{2}\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$10\sqrt{2}\times \frac{\sqrt{6}}{6}$$

10\times \frac{\sqrt{6}}{6} ni yagona kasrga aylantiring.

$$\frac{10\sqrt{6}}{6}\sqrt{2}$$

\frac{5}{3}\sqrt{6} ni olish uchun 10\sqrt{6} ni 6 ga bo‘ling.

$$\frac{5}{3}\sqrt{6}\sqrt{2}$$

Faktor: 6=2\times 3. \sqrt{2\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

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

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

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

\frac{5}{3}\times 2 ni yagona kasrga aylantiring.

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

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

$$\frac{10}{3}\sqrt{3}$$