Question

simplify 2√3/√2+√3 + 6√2/√6+√3 - 8√3/√6+√2​

Answer 1

Answer:

$2\cdot \frac{\sqrt{3}}{\sqrt{2}}+\sqrt{3}+6\cdot \frac{\sqrt{2}}{\sqrt{6}}+\sqrt{3}-8\cdot \frac{\sqrt{3}}{\sqrt{6}}+\sqrt{2}=\sqrt{6}+4\sqrt{3}-3\sqrt{2}\quad \left(\mathrm{Decimal:\quad }\:5.13505\dots \right)$

Step-by-step explanation:

$2\cdot \frac{\sqrt{3}}{\sqrt{2}}+\sqrt{3}+6\cdot \frac{\sqrt{2}}{\sqrt{6}}+\sqrt{3}-8\cdot \frac{\sqrt{3}}{\sqrt{6}}+\sqrt{2}$

$\gray{\mathrm{Group\:like\:terms}}$

$=2\cdot \frac{\sqrt{3}}{\sqrt{2}}+6\cdot \frac{\sqrt{2}}{\sqrt{6}}-8\cdot \frac{\sqrt{3}}{\sqrt{6}}+\sqrt{3}+\sqrt{3}+\sqrt{2}$

$\gray{\mathrm{Add\:similar\:elements:}\:\sqrt{3}+\sqrt{3}=2\sqrt{3}}$

$=2\cdot \frac{\sqrt{3}}{\sqrt{2}}+6\cdot \frac{\sqrt{2}}{\sqrt{6}}-8\cdot \frac{\sqrt{3}}{\sqrt{6}}+2\sqrt{3}+\sqrt{2}$

$\gray{2\cdot \frac{\sqrt{3}}{\sqrt{2}}=\sqrt{6}}$

$\gray{6\cdot \frac{\sqrt{2}}{\sqrt{6}}=2\sqrt{3}}$

$\gray{8\cdot \frac{\sqrt{3}}{\sqrt{6}}=4\sqrt{2}}$

$=\sqrt{6}+2\sqrt{3}-4\sqrt{2}+2\sqrt{3}+\sqrt{2}$

$\gray{\mathrm{Add\:similar\:elements:}\:-4\sqrt{2}+\sqrt{2}=-3\sqrt{2}}$

$=\sqrt{6}+2\sqrt{3}-3\sqrt{2}+2\sqrt{3}$

$\gray{\mathrm{Add\:similar\:elements:}\:2\sqrt{3}+2\sqrt{3}=4\sqrt{3}}$

$=\sqrt{6}+4\sqrt{3}-3\sqrt{2}$