20. Сократите дробь: а) (√6 − √2)/√8; б) (√6 + √15)/(√8 + √20); в) (10 − 2√5)/(√20 − 2); г) (4 + 2√2)/(√8 + 2).

а) \(\dfrac{\sqrt6-\sqrt2}{\sqrt8}=\dfrac{\sqrt2(\sqrt3-1)}{2\sqrt2}=\dfrac{\sqrt3-1}{2}\).

б) \(\dfrac{\sqrt6+\sqrt{15}}{\sqrt8+\sqrt{20}}=\dfrac{\sqrt3(\sqrt2+\sqrt5)}{2(\sqrt2+\sqrt5)}=\dfrac{\sqrt3}{2}\).

в) \(\dfrac{10-2\sqrt5}{\sqrt{20}-2}=\dfrac{2(5-\sqrt5)}{2(\sqrt5-1)}=\dfrac{\sqrt5(\sqrt5-1)}{\sqrt5-1}=\sqrt5\).

г) \(\dfrac{4+2\sqrt2}{\sqrt8+2}=\dfrac{2(2+\sqrt2)}{2(\sqrt2+1)}=\sqrt2\), поскольку \(2+\sqrt2=\sqrt2(\sqrt2+1)\).

Ответ: а) \(\dfrac{\sqrt3-1}{2}\); б) \(\dfrac{\sqrt3}{2}\); в) \(\sqrt5\); г) \(\sqrt2\).