Answer the following questions related to expressions whose denominators contain a…

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Answer the following questions related to expressions whose denominators contain a single square root. (i) Why is

\sqrt{m}

irrational when

m

is a positive integer that is not a perfect square? (ii) Describe, in words, the operation you would perform to write

\dfrac{p}{\sqrt{m}}

in an equivalent form that has a rational denominator. (iii) Apply the process you described in part (ii) to

\dfrac{3}{\sqrt{8}}

and write the final answer in its simplest radical form.