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Units are standards of measurement used for different types of quantities.

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Give an interpretation of what $c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}$ actually means

My intuitive understanding of electromagnetic units is rather lacking. So now I'm basically given $v=(\sqrt{\varepsilon\mu})^{-1}$ and I want an intuitive understanding why the units work out. … And please no "There are no fundamental units" philosophy, I'm asking for an intuitive grasp of the units making sense just like my pressure example was graspable and made sense. …
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