3
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$Given$:

$S$, $T$, $U$, $V$. are distinct digits which can vary from zero to nine, with $V>U$.

$ST$, $STT$ are concatenated Numbers.

Deduce S, T, U, V from the following relationship.

$$ST=\sqrt[U]{STT} \times \sqrt[V]{STT}$$

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3
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It works with

$S=1,T=0,U=3,V=6$.

We can rewrite the equation as follows:

$$ST=\sqrt[U]{STT}\times\sqrt[V]{STT}=(STT)^{1/U}\times(STT)^{1/V}=(STT)^{\frac{1}{U}+\frac{1}{V}}=(STT)^{\frac{U+V}{U\times V}}$$ $$(ST)^{U*V}=(STT)^{U+V}$$

Clearly this works if

$ST=10,STT=100$, and $U*V=2*(U+V)$,

which yields the solution stated.

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  • $\begingroup$ Great!!!...got it $\endgroup$ – Uvc Jun 14 at 15:21

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