Given the unique characteristics of neutrosophic sets for coping with uncertainties arising from incomplete information, many researchers have paired this brilliant theory with MCDM (multi-criteria decision-making) methods which have emerged as practical tool for tackling real-world decision-making problems. Root assessment method (RAM) is one of the latest MCDM methods and in this paper, new version of this method based on neutrosophic set is developed for the first time. Three of the most important features which distinguish RAM over other MCDM methods are its reliability, remarkable simplicity and ability to provide a new level of compensation between criteria. To handle the uncertainties during decision-making, we extend RAM with single valued trapezoidal neutrosophic numbers (SVTNNs) and applied it to the problem of investment selection in an uncertain environment. SVTNNs can handle various aspects of uncertainty by considering the truthiness, falsity and indeterminacy together. Results, sensitivity study and comparative study demonstrate that this version of RAM is reliable, computationally efficient and can be used to tackle various MCDM problems. The extended version of RAM with SVTNNs has a practical algorithm that expert can straightforwardly apply to deal with complicated real-world problems without requiring mathematical expertise or advanced software.