Einstein summation and square roots

Question

It has occurred to me I don't know if there is a general rule about this or not.
If I have an expression like:
$$int sqrt{g_{ij}frac{dx^i}{dt}frac{dx^j}{dt}} dt$$
I take the summation inside the square root (i.e. before performing the square root).
But is this a general rule ?  If I see $sqrt{a_{ij}}$ am I always supposed to assume the summation is done before the square root or is this very context dependent ?

Buraian · Accepted Answer

The inner expression reads:
$$ g_{ij} frac{dx^i}{dt} frac{dx^j}{dt} =  sum_{text{all}(i,j)}  g_{ij} frac{dx^i}{dt} frac{dx^j}{dt} $$
So you'd have to sum and then square root as the sum and square root operations are not interchangeable

Einstein summation and square roots

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