We are given that J is jointly proportional to G and V so: J=kGV

Solve for k when \(\displaystyle{J}=√{3}\), \(G=√2\), and \(\displaystyle{V}=√{8}\): \(\displaystyle√{3}={k}{\left(√{2}\right)}{\left(√{8}\right)}\)

\(\displaystyle√{3}={k}√{16}\)

\(\displaystyle√{3}={4}{k}\)

\(\displaystyle√\frac{{3}}{{4}}={k}\)

So, the equation becomes: \(\displaystyle{J}={\left(√\frac{{3}}{{4}}\right)}{G}{V}\)

When \(\displaystyle{G}=√{6}\) and V=8, \(\displaystyle{J}=√\frac{{3}}{{4}}{\left(√{6}\right)}{\left({8}\right)}\)

\(\displaystyle{J}={2}√{18}\)

\(\displaystyle{J}={2}√{9}\cdot{2}\)

\(\displaystyle{J}={2}\cdot{3}√{2}\)

\(\displaystyle{J}={6}√{2}\)