(10/sqrt{5}-5/sqrt{3})(2/sqrt{3}+4/sqrt{5}) eching

$$( \frac { 10 } { \sqrt { 5 } } - \frac { 5 } { \sqrt { 3 } } ) ( \frac { 2 } { \sqrt { 3 } } + \frac { 4 } { \sqrt { 5 } } )$$

Baholash

$$\frac{14}{3}\approx 4,666666667$$

Qisqa yechim qadamlari

\frac{10}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\left(\frac{10\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{5}{\sqrt{3}}\right)\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

\sqrt{5} kvadrati – 5.

$$\left(\frac{10\sqrt{5}}{5}-\frac{5}{\sqrt{3}}\right)\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

2\sqrt{5} ni olish uchun 10\sqrt{5} ni 5 ga bo‘ling.

$$\left(2\sqrt{5}-\frac{5}{\sqrt{3}}\right)\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

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

$$\left(2\sqrt{5}-\frac{5\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

\sqrt{3} kvadrati – 3.

$$\left(2\sqrt{5}-\frac{5\sqrt{3}}{3}\right)\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2\sqrt{5} ni \frac{3}{3} marotabaga ko'paytirish.

$$\left(\frac{3\times 2\sqrt{5}}{3}-\frac{5\sqrt{3}}{3}\right)\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

\frac{3\times 2\sqrt{5}}{3} va \frac{5\sqrt{3}}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3\times 2\sqrt{5}-5\sqrt{3}}{3}\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

3\times 2\sqrt{5}-5\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\left(\frac{2}{\sqrt{3}}+\frac{4}{\sqrt{5}}\right)$$

\frac{2}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\left(\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{4}{\sqrt{5}}\right)$$

\sqrt{3} kvadrati – 3.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\left(\frac{2\sqrt{3}}{3}+\frac{4}{\sqrt{5}}\right)$$

\frac{4}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\left(\frac{2\sqrt{3}}{3}+\frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)$$

\sqrt{5} kvadrati – 5.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\left(\frac{2\sqrt{3}}{3}+\frac{4\sqrt{5}}{5}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 5 ning eng kichik umumiy karralisi 15. \frac{2\sqrt{3}}{3} ni \frac{5}{5} marotabaga ko'paytirish. \frac{4\sqrt{5}}{5} ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\left(\frac{5\times 2\sqrt{3}}{15}+\frac{3\times 4\sqrt{5}}{15}\right)$$

\frac{5\times 2\sqrt{3}}{15} va \frac{3\times 4\sqrt{5}}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\times \frac{5\times 2\sqrt{3}+3\times 4\sqrt{5}}{15}$$

5\times 2\sqrt{3}+3\times 4\sqrt{5} ichidagi ko‘paytirishlarni bajaring.

$$\frac{6\sqrt{5}-5\sqrt{3}}{3}\times \frac{10\sqrt{3}+12\sqrt{5}}{15}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{6\sqrt{5}-5\sqrt{3}}{3} ni \frac{10\sqrt{3}+12\sqrt{5}}{15} ga ko‘paytiring.

$$\frac{\left(6\sqrt{5}-5\sqrt{3}\right)\left(10\sqrt{3}+12\sqrt{5}\right)}{3\times 15}$$

45 hosil qilish uchun 3 va 15 ni ko'paytirish.

$$\frac{\left(6\sqrt{5}-5\sqrt{3}\right)\left(10\sqrt{3}+12\sqrt{5}\right)}{45}$$

6\sqrt{5}-5\sqrt{3} ifodaning har bir elementini 10\sqrt{3}+12\sqrt{5} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{60\sqrt{3}\sqrt{5}+72\left(\sqrt{5}\right)^{2}-50\left(\sqrt{3}\right)^{2}-60\sqrt{3}\sqrt{5}}{45}$$

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

$$\frac{60\sqrt{15}+72\left(\sqrt{5}\right)^{2}-50\left(\sqrt{3}\right)^{2}-60\sqrt{3}\sqrt{5}}{45}$$

\sqrt{5} kvadrati – 5.

$$\frac{60\sqrt{15}+72\times 5-50\left(\sqrt{3}\right)^{2}-60\sqrt{3}\sqrt{5}}{45}$$

360 hosil qilish uchun 72 va 5 ni ko'paytirish.

$$\frac{60\sqrt{15}+360-50\left(\sqrt{3}\right)^{2}-60\sqrt{3}\sqrt{5}}{45}$$

\sqrt{3} kvadrati – 3.

$$\frac{60\sqrt{15}+360-50\times 3-60\sqrt{3}\sqrt{5}}{45}$$

-150 hosil qilish uchun -50 va 3 ni ko'paytirish.

$$\frac{60\sqrt{15}[phone]\sqrt{3}\sqrt{5}}{45}$$

210 olish uchun 360 dan 150 ni ayirish.

$$\frac{60\sqrt{15}+210-60\sqrt{3}\sqrt{5}}{45}$$

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

$$\frac{60\sqrt{15}+210-60\sqrt{15}}{45}$$

0 ni olish uchun 60\sqrt{15} va -60\sqrt{15} ni birlashtirish.

$$\frac{210}{45}$$

\frac{210}{45} ulushini 15 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{14}{3}$$

Omil

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4,666666666666667$$