Mathematics

Problem

Consider the following expressions involving square roots. a. (i) Express

5\sqrt{12}

as a single square root. b. (ii) Simplify

\sqrt{3}\times\sqrt{75}

and express the answer in the form

c\sqrt{d}

, where

d

is square-free. c. (iii) Hence evaluate

\dfrac{5\sqrt{12}}{\sqrt{3}\,\sqrt{75}}

and simplify your answer as far as possible.