Mathematics

Problem

Answer the following questions concerning squares and nth roots. a. (i) State the meaning of

\sqrt[n]{a}

for a positive real number

a

and a natural number

n

. b. (ii) If the area of a square is

A\,\text{square units}

, show that the length of one side of the square is

\sqrt{A}\,\text{units}

. c. (iii) The area of a square sheet of paper is

128\,\text{cm}^2

. Express the length of its side in simplest radical form and explain why this length is an irrational number.