<p>Show that&nbsp;\( \left( \sqrt{2} + \sqrt{3} + \sqrt{6} \right)^2 = 11 + 6\sqrt{2} + 4\sqrt{3} + 2\sqrt{6}\). <br>Hence or otherwise, determine whether there exist rational numbers \(a, b, c, d\) such that&nbsp;\( \sqrt{11 + 6\sqrt{2} + 4\sqrt{3} 2\sqrt{6}} = a + b\sqrt{2} + c\sqrt{3} + d\sqrt{6}\), if they exist, find them.</p>

Show that \( \left( \sqrt{2} + \sqrt{3} + \sqrt{6} \right)^2 = 11 + 6\sqrt{2} + 4\sqrt{3} + 2\sqrt{6}\). 
Hence or otherwise, determine whether there exist rational numbers \(a, b, c, d\) such that \( \sqrt{11 + 6\sqrt{2} + 4\sqrt{3} 2\sqrt{6}} = a + b\sqrt{2} + c\sqrt{3} + d\sqrt{6}\), if they exist, find them.

Surds

Surds