Let $\overrightarrow{u}, \overrightarrow{v}$ and $\overrightarrow{w}$ be vectors in three-dimensional space, where $\overrightarrow{u}$ and $\overrightarrow{v}$ are unit vectors which are not perpendicular to each other and $\overrightarrow{u}.\overrightarrow{w}=\frac{3}{2},\overrightarrow{v}.\overrightarrow{w}=2,\overrightarrow{w}.\overrightarrow{w}=9.$ If the volume of the parallelepiped, whose adjacent sides are represented by the vectors $\overrightarrow{u},\overrightarrow{v}$ and $\overrightarrow{w}$ is $\sqrt{\frac{7}{2}},$ then the value of $|3\overrightarrow{u}+5\overrightarrow{v}|$ is _____________ (It is given that angle between $\overrightarrow{u}$ and $\overrightarrow{v}$ is acute and less than $\frac{5\pi }{12}$ )