Mathematics

Problem

Let

a

be a positive integer that is not a perfect square and let

k

be a non–zero integer. a. (i) Show that

\sqrt{a}\times\dfrac{1}{\sqrt{a}}=1

. b. (ii) Using the result of part (i), derive a general expression, in simplest form, for

\dfrac{1}{k\sqrt{a}}

that has a rational denominator. c. (iii) Apply your expression from part (ii) to write

\dfrac{1}{5\sqrt{11}}

and

\dfrac{1}{-3\sqrt{20}}

with rational denominators.