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The London penetration depth, $\lambda(T)$, was measured in a single crystalV$_{3}$Si. The superfluid density obtained from this measurement shows adistinct signature of two almost decoupled superconducting gaps. This alone isinsufficient to distinguish between $s_{\pm}$ and $s_{++}$ pairing states, butit can be achieved by studying the effect of a controlled non-magnetic disorderon the superconducting transition temperature, $T_{c}$. For this purpose, thesame $\text{V}_{3}\text{Si}$ crystal was sequentially irradiated by 2.5 MeVelectrons three times, repeating the measurement between the irradiation runs.A total dose of 10 C/cm$^{2}$ ($6.24\times10^{19}$ electrons/$\textrm{cm}^{2}$)was accumulated, for which $T_{c}$ has changed from 16.4 K in a pristine stateto 14.7 K (9.3 $\%$). This substantial suppression is impossible for a singleisotropic gap, but also it is not large enough for a sign-changing $s_{\pm}$pairing state. Our electronic band-structure calculations show how five bandscrossing the Fermi energy can be naturally grouped to support two effectivegaps, not dissimilar from the iron pnictides physics. We analyze the resultsusing two-gap models for both, $\lambda(T)$ and $T_{c}$, which describe thedata very well. Thus, the experimental results and theoretical analysis providestrong support for an $s_{++}$ superconductivity with two unequal gaps,$\Delta_{1}\left(0\right)\approx2.53\;\textrm{meV}$ and$\Delta_{2}\left(0\right)\approx1.42\;\textrm{meV}$, and a very weak inter-bandcoupling in $\text{V}_{3}\text{Si}$ superconductor.

Multi-band $s_{++}$ superconductivity in $\textrm{V}_{3}\textrm{Si}$ determined from the response to a controlled disorder