bài1 a) \(\sqrt{2}+\sqrt{50}-3\sqrt{18}\)=\(\sqrt{2}+5\sqrt{2}-9\sqrt{2}\)=-3\(\sqrt{2}\)
b)\(\dfrac{6}{\sqrt{5}-1}=\dfrac{6\cdot\left(\sqrt{5}+1\right)}{5-1}=\dfrac{6\sqrt{5}+6}{4}=\dfrac{3+3\sqrt{5}}{2}\)
c)\(6\sqrt{\dfrac{1}{2}}=\sqrt{36\cdot\dfrac{1}{2}}=\sqrt{\dfrac{36}{2}}=\sqrt{18}=3\sqrt{2}\)
d)\(\sqrt{6-3x}\)có nghĩa khi 6-3x\(\ge\)0\(\Leftrightarrow-3x\ge-6\Leftrightarrow x\le2\)
bài2
a)\(\sqrt{\left(\sqrt{7}-3\right)^2}-1+\sqrt{7}=-\sqrt{7}+3-1+\sqrt{7}=2\)
b)\(\dfrac{3-\sqrt{3}}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}=3-\dfrac{\left(3-\sqrt{3}\right)\cdot\left(\sqrt{3}+1\right)}{3-1}-\dfrac{2\left(\sqrt{3}-1\right)}{3-1}\)
=\(\dfrac{3\sqrt{3}+3-3-\sqrt{3}}{2}\dfrac{2\sqrt{3}-2}{2}=\dfrac{4\sqrt{3}-2}{2}\)\(-1+2\sqrt{3}\)
bài3
1-\(\sqrt{x-3}=\sqrt{4x-12}-5\)\(\Leftrightarrow1-\sqrt{x-3}=2\sqrt{x-3}-5\Leftrightarrow-\sqrt{x-3}-2\sqrt{x-3}=-1-5\)
\(\Leftrightarrow-3\sqrt{x-3}=-6\)\(\sqrt{x-3}=2\Leftrightarrow x-3=4\Leftrightarrow x=3+4\Leftrightarrow x=7\)
