The choice which is equivalent to [tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}[/tex] is given by (A) [tex]\frac{\sqrt{x}}{2}[/tex].
What is expression?
Expression is a mathematical term that involves variables, numbers and other mathematical quantities and operations or combinations of them.
The given expression is [tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}[/tex]
Calculating the expression we get,
[tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}=\sqrt{\frac{2}{x}\cdot\frac{x^2}{8}}=\sqrt{\frac{x}{4}}=\frac{\sqrt{x}}{2}[/tex]
So the expression equals to [tex]\frac{\sqrt{x}}{2}[/tex].
Hence the correct option is (A).
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