So [a+( 1/a)]2 square = 10=a2 square+1/a2 square +2.

A2 square+1/a2 square = 10-2=8

So the square of [a-( 1/a)]2 =a2+ 1/a2-2=8-2=6.

So the square of a-(1/a) = √ [a-(1/a)] 2 = √ 6.