2/sqrt{6}*1/sqrt{3^3} eching

$$\frac{ 2 }{ \sqrt{ 6 } } \times \frac{ 1 }{ \sqrt{ { 3 }^{ 3 } } }$$

Baholash

$$\frac{\sqrt{2}}{9}\approx 0,15713484$$

Yechim qadamlari

\frac{2}{\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\times \frac{1}{\sqrt{3^{3}}}$$

\sqrt{6} kvadrati – 6.

$$\frac{2\sqrt{6}}{6}\times \frac{1}{\sqrt{3^{3}}}$$

\frac{1}{3}\sqrt{6} ni olish uchun 2\sqrt{6} ni 6 ga bo‘ling.

$$\frac{1}{3}\sqrt{6}\times \frac{1}{\sqrt{3^{3}}}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$\frac{1}{3}\sqrt{6}\times \frac{1}{\sqrt{27}}$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{1}{3}\sqrt{6}\times \frac{1}{3\sqrt{3}}$$

\frac{1}{3\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{1}{3}\sqrt{6}\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{1}{3}\sqrt{6}\times \frac{\sqrt{3}}{3\times 3}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$\frac{1}{3}\sqrt{6}\times \frac{\sqrt{3}}{9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{3} ni \frac{\sqrt{3}}{9} ga ko‘paytiring.

$$\frac{\sqrt{3}}{3\times 9}\sqrt{6}$$

27 hosil qilish uchun 3 va 9 ni ko'paytirish.

$$\frac{\sqrt{3}}{27}\sqrt{6}$$

\frac{\sqrt{3}}{27}\sqrt{6} ni yagona kasrga aylantiring.

$$\frac{\sqrt{3}\sqrt{6}}{27}$$

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

$$\frac{\sqrt{3}\sqrt{3}\sqrt{2}}{27}$$

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

$$\frac{3\sqrt{2}}{27}$$

\frac{1}{9}\sqrt{2} ni olish uchun 3\sqrt{2} ni 27 ga bo‘ling.

$$\frac{1}{9}\sqrt{2}$$