Mathematics

Problem

A square piece of cardboard has area

512\,\text{cm}^2

. Each side of the square is enlarged by a factor of

2^{1/4}

to form a bigger square. Answer the following. a. (i) Find the length of a side of the original square in its simplest radical form. b. (ii) Determine the length of a side of the enlarged square, expressing your answer as a power of

2

with a rational exponent. c. (iii) Calculate the area of the enlarged square and simplify it to the form

2^{k}

. State the value of

k

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