Question

Plzz help me to solve this sum

Answer 1

rationalize each fraction by multiplying the numerator and denominator with the conjugate of the denominator.

$\frac{7\sqrt3}{\sqrt{10}+\sqrt3} - \frac{2\sqrt5}{\sqrt6+\sqrt5} - \frac{3\sqrt2}{\sqrt{15}+3\sqrt2} \\\\=\frac{7\sqrt3*(\sqrt{10}-\sqrt3)}{(\sqrt{10}+\sqrt3)*(\sqrt{10}-\sqrt3)} - \frac{2\sqrt5*(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)*(\sqrt6-\sqrt5)} - \frac{3\sqrt2*(\sqrt{15}-3\sqrt2)}{(\sqrt{15}+3\sqrt2)*(\sqrt{15}-3\sqrt2)} \\\\=\frac{7\sqrt{30}-7*3}{10-3}-\frac{2\sqrt{30}-2*5}{6-5}-\frac{3\sqrt{30}-9*2}{15-9*2}\\\\=\sqrt{30}-3-2\sqrt{30}+10+\sqrt{30}-6\\\\=1$