frac{sqrt{3}}{sqrt{5}}-frac{sqrt{5}+sqrt{30}}{sqrt{2}} eching

$$\frac { \sqrt { 3 } } { \sqrt { 5 } } - \frac { \sqrt { 5 } + \sqrt { 30 } } { \sqrt { 2 } }$$

Baholash

$$-\frac{\sqrt{10}}{2}-\frac{4\sqrt{15}}{5}\approx -4,679525507$$

Qisqa yechim qadamlari

\frac{\sqrt{3}}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}}$$

\sqrt{3} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{15}}{5}-\frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}}$$

\frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{15}}{5}-\frac{\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\sqrt{15}}{5}-\frac{\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{2}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 va 2 ning eng kichik umumiy karralisi 10. \frac{\sqrt{15}}{5} ni \frac{2}{2} marotabaga ko'paytirish. \frac{\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{2} ni \frac{5}{5} marotabaga ko'paytirish.

$$\frac{2\sqrt{15}}{10}-\frac{5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{10}$$

\frac{2\sqrt{15}}{10} va \frac{5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{10} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2\sqrt{15}-5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{10}$$

2\sqrt{15}-5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{2\sqrt{15}-5\sqrt{10}-10\sqrt{15}}{10}$$

2\sqrt{15}-5\sqrt{10}-10\sqrt{15} hisob-kitobini qiling.

$$\frac{-8\sqrt{15}-5\sqrt{10}}{10}$$