MCQ
Simplify: $\frac{7\sqrt3}{\sqrt10+\sqrt3}-\frac{2\sqrt5}{\sqrt6+\sqrt5}-\frac{3\sqrt2}{\sqrt15+3\sqrt2}$
- A$0$
- ✓$1$
- C$2$
- D$3$
$\frac{7\sqrt3}{\sqrt10+\sqrt3}-\frac{2\sqrt5}{\sqrt6+\sqrt5}-\frac{3\sqrt2}{\sqrt15+3\sqrt2}$
$=\frac{7\sqrt3\big(\sqrt10-\sqrt3\big)}{\big(\sqrt10+\sqrt3\big)\big(\sqrt10-\sqrt3\big)}-\frac{2\sqrt5\big(\sqrt6-\sqrt5\big)}{\big(\sqrt6+\sqrt5\big)\big(\sqrt6-\sqrt5\big)}-\frac{3\sqrt2\big(\sqrt15-3\sqrt2\big)}{\big(\sqrt15-3\sqrt2\big)\big(\sqrt15+3\sqrt2\big)}$
$=\frac{7\sqrt3\big(\sqrt10-\sqrt3\big)}{10-3}-\frac{2\sqrt5\big(\sqrt6-\sqrt5\big)}{6-5}-\frac{3\sqrt2\big(\sqrt15-3\sqrt2\big)}{15-18}$
$=\frac{7\sqrt3\big(\sqrt10-\sqrt3\big)}{7}-\frac{2\sqrt5\big(\sqrt6-\sqrt5\big)}{1}-\frac{3\sqrt2\big(\sqrt15-3\sqrt2\big)}{3}$
$=\frac{21\sqrt30-63425\sqrt30+210+21\sqrt30-18*7}{21}$
$=\frac{21}{21}=1$
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