Surds - Applications of Surds

A rectangular block has a square base. The length of each side of the base is \(\left( \sqrt{5}-\sqrt{3} \right)\mathrm{ m}\) and the volume of the block is \(\left( 4\sqrt{3}-2\sqrt{5} \right)\mathrm{ }{{\mathrm{m}}^{\mathrm{3}}}\). Find, without the use of a calculator, the height of the block in the form of \(a\sqrt{3}+b\sqrt{5}\).