2/sqrt{3}+12/sqrt{27}+2sqrt{7} eching

$$\frac { 2 } { \sqrt { 3 } } + \frac { 12 } { \sqrt { 27 } } + 2 \sqrt { 7 }$$

Baholash

$$2\left(\sqrt{3}+\sqrt{7}\right)\approx 8,755604237$$

Yechim qadamlari

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

$$\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{12}{\sqrt{27}}+2\sqrt{7}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\sqrt{3}}{3}+\frac{12}{\sqrt{27}}+2\sqrt{7}$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{2\sqrt{3}}{3}+\frac{12}{3\sqrt{3}}+2\sqrt{7}$$

\frac{12}{3\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{3}}{3}+\frac{12\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}+2\sqrt{7}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\sqrt{3}}{3}+\frac{12\sqrt{3}}{3\times 3}+2\sqrt{7}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{2\sqrt{3}}{3}+\frac{4\sqrt{3}}{3}+2\sqrt{7}$$

2\sqrt{3} ni olish uchun \frac{2\sqrt{3}}{3} va \frac{4\sqrt{3}}{3} ni birlashtirish.

$$2\sqrt{3}+2\sqrt{7}$$

Omil

$$2 {(\sqrt{3} + \sqrt{7})} = 8,755604237$$