a)
\(\sqrt{2}.x - \sqrt{50} = 0\)
\(\Leftrightarrow \sqrt{2}x=\sqrt{50}\)
\(\Leftrightarrow x=\dfrac{\sqrt{50}}{\sqrt{2}}\)
\(\Leftrightarrow x =\sqrt{\dfrac{50}{2}}\)
\(\Leftrightarrow x= \sqrt{25}\)
\(\Leftrightarrow x= \sqrt{5^2}\)
\(\Leftrightarrow x=5\).
Vậy \(x=5\).
b)
\(\sqrt{3}.x + \sqrt{3} = \sqrt{12} + \sqrt{27}\)
\( \Leftrightarrow \sqrt{3}.x = \sqrt{12} + \sqrt{27} - \sqrt{3}\)
\(\Leftrightarrow \sqrt{3}.x=\sqrt{4.3}+\sqrt{9.3}- \sqrt{3}\)
\(\Leftrightarrow \sqrt{3}.x=\sqrt{4}. \sqrt{3}+\sqrt{9}. \sqrt{3}- \sqrt{3}\)
\(\Leftrightarrow \sqrt{3}.x=\sqrt{2^2}. \sqrt{3}+\sqrt{3^2}. \sqrt{3}- \sqrt{3}\)
\(\Leftrightarrow \sqrt{3}.x=2 \sqrt{3}+3\sqrt{3}- \sqrt{3}\)
\(\Leftrightarrow \sqrt{3}.x=(2+3-1).\sqrt{3}\)
\(\Leftrightarrow \sqrt{3}.x=4\sqrt{3}\)
\(\Leftrightarrow x=4\).
Vậy \(x=4\).
c)
\(\sqrt{3}x^2-\sqrt{12}=0\)
\(\Leftrightarrow \sqrt{3}x^2=\sqrt{12}\)
\(\Leftrightarrow \sqrt{3}x^2=\sqrt{4.3}\)
\(\Leftrightarrow \sqrt{3}x^2=\sqrt{4}.\sqrt 3\)
\(\Leftrightarrow x^2=\sqrt{4}\)
\(\Leftrightarrow x^2=\sqrt{2^2}\)
\(\Leftrightarrow x^2=2\)
\(\Leftrightarrow \sqrt{x^2}=\sqrt{2}\)
\(\Leftrightarrow |x|= \sqrt 2\)
\(\Leftrightarrow x= \pm \sqrt 2\).
Vậy \(x= \pm\sqrt 2\).
d)
\(\dfrac{x^{2}}{\sqrt{5}}- \sqrt{20} = 0\)
\(\Leftrightarrow \dfrac{x^2}{\sqrt{5}}=\sqrt{20}\)
\(\Leftrightarrow x^2=\sqrt{20}.\sqrt{5}\)
\(\Leftrightarrow x^2=\sqrt{20.5}\)
\(\Leftrightarrow x^2=\sqrt{100}\)
\(\Leftrightarrow x^2=\sqrt{10^2}\)
\(\Leftrightarrow x^2=10\)
\(\Leftrightarrow \sqrt{x^2}=\sqrt {10}\)
\(\Leftrightarrow |x|=\sqrt{10}\)
\(\Leftrightarrow x=\pm \sqrt{10}\).
Vậy \(x= \pm \sqrt{10}\).
