Đáp án: $a)=1$
$b)=8$
Giải thích các bước giải:
$a)\sqrt{(3-\sqrt{6})^2}+\sqrt{10-4\sqrt{6}}$
$=|3-\sqrt{6}|+\sqrt{6-2.2.\sqrt{6}+4}$
$=(3-\sqrt{6})+\sqrt{(\sqrt{6}-2)^2}$
$=3-\sqrt{6}+|\sqrt{6}-2|$
$=3-\sqrt{6}+(\sqrt{6}-2)$
$=3-\sqrt{6}+\sqrt{6}-2=1$
$b)\sqrt{3-\sqrt{5}}.(\sqrt{10}-\sqrt{2})(3+\sqrt{5})$
$=\sqrt{3-\sqrt{5}}.\sqrt{2}.(\sqrt{5}-1)(3+\sqrt{5})$
$=\sqrt{6-2\sqrt{5}}.(\sqrt{5}-1)(3+\sqrt{5})$
$=\sqrt{5-2\sqrt{5}+1}.(\sqrt{5}-1)(3+\sqrt{5})$
$=\sqrt{(\sqrt{5}-1)^2}.(\sqrt{5}-1)(3+\sqrt{5})$
$=|\sqrt{5}-1|.(\sqrt{5}-1)(3+\sqrt{5})$
$=(\sqrt{5}-1)(\sqrt{5}-1)(3+\sqrt{5})$
$=(\sqrt{5}-1)^2(3+\sqrt{5})$
$=(6-2\sqrt{5})(3+\sqrt{5}$
$=2(3-\sqrt{5})(3+\sqrt{5})$
$=2(9-5)=2.4=8$
