frac{3sqrt{10}}{10}*frac{sqrt{5}}{5}+frac{sqrt{10}}{10}*frac{2sqrt{15}}{5} eching

$$\frac { 3 \sqrt { 10 } } { 10 } \times \frac { \sqrt { 5 } } { 5 } + \frac { \sqrt { 10 } } { 10 } \times \frac { 2 \sqrt { 15 } } { 5 }$$

Baholash

$$\frac{\sqrt{2}\left(2\sqrt{3}+3\right)}{10}\approx 0,914162017$$

Qisqa yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3\sqrt{10}}{10} ni \frac{\sqrt{5}}{5} ga ko‘paytiring.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}}{10}\times \frac{2\sqrt{15}}{5}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{10}}{10} ni \frac{2\sqrt{15}}{5} ga ko‘paytiring.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\times 2\sqrt{15}}{10\times 5}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{3\sqrt{10}\sqrt{5}}{10\times 5}+\frac{\sqrt{10}\sqrt{15}}{5\times 5}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5\times 5 ni kengaytirish.

$$\frac{3\sqrt{10}\sqrt{5}}{5\times 10}+\frac{\sqrt{10}\sqrt{15}}{5\times 10}$$

\frac{3\sqrt{10}\sqrt{5}}{5\times 10} va \frac{\sqrt{10}\sqrt{15}}{5\times 10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3\sqrt{10}\sqrt{5}+\sqrt{10}\sqrt{15}}{5\times 10}$$

3\sqrt{10}\sqrt{5}+\sqrt{10}\sqrt{15} ichidagi ko‘paytirishlarni bajaring.

$$\frac{15\sqrt{2}+5\sqrt{6}}{5\times 10}$$

5\times 10 ni kengaytirish.

$$\frac{15\sqrt{2}+5\sqrt{6}}{50}$$

Omil

$$\frac{\sqrt{2} {(\sqrt{2} \sqrt{6} + 3)}}{10} = 0,9141620172685642$$