Lời giải:
b.
$\sqrt{3(2-\sqrt{5})^2}=|\sqrt{3}(2-\sqrt{5})|=\sqrt{3}(\sqrt{5}-2)$
$\sqrt{18(2-\sqrt{3})^2}=|\sqrt{18}(2-\sqrt{3})|$
$=\sqrt{18}(2-\sqrt{3})=-3\sqrt{6}+6\sqrt{2}$
\(\sqrt{\frac{5(1-\sqrt{3})^2}{4}}=\sqrt{(\frac{\sqrt{5}(1-\sqrt{3})}{2})^2}=|\frac{\sqrt{5}(1-\sqrt{3})}{2}|\)
\(=\frac{\sqrt{5}(\sqrt{3}-1)}{2}\)
c.
\(\sqrt{\frac{8}{(1-\sqrt{2})^2}}=\sqrt{(\frac{2\sqrt{2}}{1-\sqrt{2}})^2}=|\frac{2\sqrt{2}}{1-\sqrt{2}}|=\frac{2\sqrt{2}}{\sqrt{2}-1}=4+2\sqrt{2}\)
\(\sqrt{(1-x)^3}=(1-x)\sqrt{1-x}\)
$x>3$ thì $x^3(1-\sqrt{3})^3< 0$ nên không tồn tại căn thức này.
d.
\(\sqrt{50(5+a)^5}=\sqrt{2.25(5+a)^4}=5(5+a)^2\sqrt{2(5+a)}\)
\(\sqrt{(x-4)^3(1-x)^5}=\sqrt{(4-x)^3(x-1)^5}=(4-x)(x-1)^2\sqrt{(4-x)(x-1)}\)
