I have a devilish problem for you, at least it was for me.

There is a square, the length of its sides are unknown.

Another, smaller, square is formed within the first square, its sides are connected by points placed at the mid point of each line of the first square.

Visually it looks like a diamond in a square.

You are told that a side (and thus all sides) of the smaller square are root 6 in length (a surd).

The object is to define the perimeter of the first, larger, square in surd form.

I started by defining the length between one of the vertices of the first square and the mid point of the line to the next (where it intersects with the smaller square) as n.

It became apparent to me that root 2 x n squared was equal to root 6.

It was also apparent that n over root 6 was equal to the inverse sin of 45 degrees.

In spite of this I am still no closer to defining n in surd form. Obviously 8n would be equal to the perimeter of the large square.

Please help...