Surds - Applications of Surds

A cylinder has a volume of \(\left( 21\sqrt{2}+17\sqrt{3} \right)\pi \mathrm{ c}{{\mathrm{m}}^{\mathrm{3}}}\) and a radius of \(\left( \sqrt{2}+\sqrt{3} \right)\mathrm{ cm}\).

Find the height of the cylinder in the form \(\left( a\sqrt{2}+b\sqrt{3} \right)\mathrm{ cm}\), where \(a\) and \(b\) are integers.