1/sqrt{5+2}+1/3sqrt{8} eching

$$\frac{ 1 }{ \sqrt{ 5+2 } } + \frac{ 1 }{ 3 \sqrt{ 8 } }$$

Baholash

$$\frac{\sqrt{7}\left(\sqrt{14}+12\right)}{84}\approx 0,495815603$$

Qisqa yechim qadamlari

7 olish uchun 5 va 2'ni qo'shing.

$$\frac{1}{\sqrt{7}}+\frac{1}{3\sqrt{8}}$$

\frac{1}{\sqrt{7}} maxrajini \sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}+\frac{1}{3\sqrt{8}}$$

\sqrt{7} kvadrati – 7.

$$\frac{\sqrt{7}}{7}+\frac{1}{3\sqrt{8}}$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{7}}{7}+\frac{1}{3\times 2\sqrt{2}}$$

6 hosil qilish uchun 3 va 2 ni ko'paytirish.

$$\frac{\sqrt{7}}{7}+\frac{1}{6\sqrt{2}}$$

\frac{1}{6\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{6\times 2}$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$\frac{\sqrt{7}}{7}+\frac{\sqrt{2}}{12}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 7 va 12 ning eng kichik umumiy karralisi 84. \frac{\sqrt{7}}{7} ni \frac{12}{12} marotabaga ko'paytirish. \frac{\sqrt{2}}{12} ni \frac{7}{7} marotabaga ko'paytirish.

$$\frac{12\sqrt{7}}{84}+\frac{7\sqrt{2}}{84}$$

\frac{12\sqrt{7}}{84} va \frac{7\sqrt{2}}{84} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{12\sqrt{7}+7\sqrt{2}}{84}$$

Omil

$$\frac{\sqrt{7} {(\sqrt{2} \sqrt{7} + 12)}}{84} = 0,49581560320698514$$