Question

Освободитесь от иррациональности в знаменателе дроби: a/√3; 3/√11-√2

Answer 1

$\frac{a}{\sqrt{3}}=\frac{a\sqrt{3}}{\sqrt{3}*\sqrt{3}}=\frac{a\sqrt{3}}{3}$
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$\frac{3}{\sqrt{11}-\sqrt{2}}=\frac{3*(\sqrt{11}+\sqrt{2})}{(\sqrt{11}-\sqrt{2})*(\sqrt{11}+\sqrt{2})}$
$=\frac{3*(\sqrt{11}+\sqrt{2})}{(\sqrt{11})^2-(\sqrt{2})^2}$
$=\frac{3*(\sqrt{11}+\sqrt{2})}{11-2}$
$=\frac{3*(\sqrt{11}+\sqrt{2})}{9}=$
$\frac{\sqrt{11}+\sqrt{2}}{3}$