I have seen the following mathematical errors for years in physics classes.

• \(\sqrt{16ab} = 4ab \)

The correct one should be \(\sqrt{16ab} = 4\sqrt{ab} \).

• \(\frac{10^{-8}}{2} = 5^{-8} \)

The above must be \(10^{-8}/2 = 0.5 \times 10^{-8} \).

• \(\frac{10^{-10}}{10^{-5}} = 10^{-15} \)

This is wrong. The right equation is: \((10^{-10})/(10^{-5}) = 10^{-5} \).

• \(\log AB = \log A \log B \)

The correct expression should be \(\log AB = \log A + \log B \).

• \(\sin (A+B) = \sin A +\sin B \)

The right equation is \(\sin (A+B) = \sin A \cos B + \sin B \cos A \).

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