Giải thích các bước giải:
a.Ta có:
$\dfrac{\sqrt{27+7\sqrt{5}}}{\sqrt{2}}$
$=\dfrac{\sqrt{54+14\sqrt{5}}}{2}$
$=\dfrac{\sqrt{7^2+2.7.\sqrt{5}+5}}{2}$
$=\dfrac{\sqrt{(7+\sqrt{5})^2}}{2}$
$=\dfrac{7+\sqrt{5}}{2}$
b.Ta có:
$\dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{2}}$
$=\dfrac{\sqrt{6-2\sqrt{5}}}{2}$
$=\dfrac{\sqrt{5-2\sqrt{5}-1}}{2}$
$=\dfrac{\sqrt{(\sqrt{5}-1)^2}}{2}$
$=\dfrac{\sqrt{5}-1}{2}$
