$S$, $T$, $U$, $V$. 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.

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


It works with


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.

  • $\begingroup$ Great!!!...got it $\endgroup$
    – Uvc
    Jun 14 '19 at 15:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.