Question

What must be subtracted from $1729$ to get a perfect square?

Answer 1

We can find out the smallest number that must be subtracted from $1729$ to get a prefect square by long division method of finding the square root....(0.5 marks)

Applying the long division method on $1729$:

$\begin{array}{ccc}& 41& \\ 4& \overline{17}\overline{29}& \\ & 16& \\ 81& 129& \\ & 81& \\ & 48& \end{array}$
...(2 marks)

We can observe that the remainder is $48$.

So, if we subtract $48$ from $1729$ we will get a perfect square.
$\Rightarrow 1729-48=1681$...(0.5 marks)

So, $48$ must be subtracted from $1729$ to get a perfect square....(0.5 marks)