\(1,024\) trees are planted in a farm such that the number of rows is equal to the number of columns. If one row and one column of trees are removed, then find the number of trees that were removed.

Number of trees \(= 1024\).

Since number of rows \(=\) number of columns, the trees are planted in a square.

Therefore number of rows/columns \(=\sqrt{1024}\)...(1 mark)

\(\sqrt{1024}=\) \(\sqrt{2\times2\times2\times2\times2\times2\times2\times2\times2 \times2}\)

\(\sqrt{1024}=32\)...(1 mark)

Number of rows/columns after removing the trees \(= 32 -1 = 31\)...(0.5 marks)
\(\therefore\) remaining number of trees \(=31^2\)...(0.5 marks)
Therefore, number of trees that were removed = \( 32^2 - 31^2 = (32+31) = 63\)....(1 mark)
[From the identity \((n+1)^2\) - \((n)^2 = (n+1) + n)\)]