(frac{sqrt{5}}{sqrt{6}}-frac{sqrt{2}}{sqrt{15}})^2 eching

$$( \frac { \sqrt { 5 } } { \sqrt { 6 } } - \frac { \sqrt { 2 } } { \sqrt { 15 } } ) ^ { 2 }$$

Baholash

$$\frac{3}{10}=0,3$$

Yechim qadamlari

\frac{\sqrt{5}}{\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}-\frac{\sqrt{2}}{\sqrt{15}}\right)^{2}$$

\sqrt{6} kvadrati – 6.

$$\left(\frac{\sqrt{5}\sqrt{6}}{6}-\frac{\sqrt{2}}{\sqrt{15}}\right)^{2}$$

\sqrt{5} va \sqrt{6} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{2}}{\sqrt{15}}\right)^{2}$$

\frac{\sqrt{2}}{\sqrt{15}} maxrajini \sqrt{15} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}\right)^{2}$$

\sqrt{15} kvadrati – 15.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{2}\sqrt{15}}{15}\right)^{2}$$

\sqrt{2} va \sqrt{15} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{30}}{15}\right)^{2}$$

\frac{1}{10}\sqrt{30} ni olish uchun \frac{\sqrt{30}}{6} va -\frac{\sqrt{30}}{15} ni birlashtirish.

$$\left(\frac{1}{10}\sqrt{30}\right)^{2}$$

\left(\frac{1}{10}\sqrt{30}\right)^{2} ni kengaytirish.

$$\left(\frac{1}{10}\right)^{2}\left(\sqrt{30}\right)^{2}$$

2 daraja ko‘rsatkichini \frac{1}{10} ga hisoblang va \frac{1}{100} ni qiymatni oling.

$$\frac{1}{100}\left(\sqrt{30}\right)^{2}$$

\sqrt{30} kvadrati – 30.

$$\frac{1}{100}\times 30$$

\frac{3}{10} hosil qilish uchun \frac{1}{100} va 30 ni ko'paytirish.

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

Omil

$$\frac{3}{2 \cdot 5} = 0,3$$