Mathematics

Problem

Three expressions are given below:

A=\sqrt{5},\;B=\dfrac{\sqrt{20}}{2},\;C=\dfrac{\sqrt{45}}{3}

. a. (i) Simplify

B

to its simplest radical form. b. (ii) Simplify

C

to its simplest radical form. c. (iii) Using the simplified forms, arrange

A,\,B,

and

C

in descending order, justifying each step of your comparison.