Bài 1:
a) \(\sqrt{14^2}=\left|14\right|=14\)
b) \(\sqrt{\left(-25\right)^2}=\left|-25\right|=25\)
Bài 2:
a) \(\sqrt{\left(3-\sqrt{2}\right)^2}=\left|3-\sqrt{2}\right|=3-\sqrt{2}\)
b) \(\sqrt{\left(1+\sqrt{5}\right)^2}=\left|1+\sqrt{5}\right|=1+\sqrt{5}\)
c) \(\sqrt{\left(1-\sqrt{3}\right)^2}=\left|1-\sqrt{3}\right|=\sqrt{3}-1\)
d) \(\sqrt{\left(a-3\right)^2}+\sqrt{\left(a-1\right)^2}=\left|a-3\right|+\left|a-1\right|\)
\(=\left[{}\begin{matrix}a-3+a-1=2a-4\left(a\ge3\right)\\3-a+a-1=2\left(3>a\ge1\right)\\3-a+1-a=4-2a\left(a< 1\right)\end{matrix}\right.\)
Bài 3:
a) \(\sqrt{3x-6}=3\left(đk:x\ge2\right)\)
\(\Leftrightarrow3x-6=9\Leftrightarrow3x=15\Leftrightarrow x=5\)
b) \(\dfrac{1}{4}\sqrt{x+5}=1\left(đk:x\ge-5\right)\)
\(\Leftrightarrow\sqrt{x+5}=4\)
\(\Leftrightarrow x+5=16\Leftrightarrow x=11\)
