Rationalise the denominator of [tex]\frac{1}{5-\sqrt{2} }[/tex] giving your answer in its simplest form.

Answer:[tex]\frac{5+\sqrt{2} }{23}[/tex]Step-by-step explanation:In this problem multiply both the top and bottom by 5 + [tex]\sqrt{2}[/tex]   I believe this is called a conjugate but im not sure.  Basically you multiply it by the denominator but the addition or subtraction sign in the middle is flipped to the opposite. This results in the removal of the root in the denominator when multiplied and you end up with the square of each of the two numbers in the denominator with varying results as far as whether its addition or subtraction