3. Answer this question without the use of a calculator and show all your working.
- Show that
$$( 5 - \sqrt { 8 } ) ( 1 + \sqrt { 2 } ) \equiv a + b \sqrt { 2 }$$
giving the values of the integers \(a\) and \(b\).
- Show that
$$\sqrt { 80 } + \frac { 30 } { \sqrt { 5 } } \equiv c \sqrt { 5 } , \text { where } c \text { is an integer. }$$