A gardener wants to plant 17956 trees in his garden and arranges them in such…

Concept

When identical objects are arranged in a square grid with the number of items in each row equal to the number of rows, the total count equals (items per row)². So if a total T forms such a perfect square arrangement, the number per row is the square root √T — the value that, multiplied by itself, gives T.

Application

Let r be the number of trees in one row. Then rows = r as well, so total = r2 = 17956. Solve for r = √17956 by prime-factor pairing:

1. Factorise: 17956 = 2 × 2 × 67 × 67.

2. Group into equal pairs: 17956 = (2 × 67)2 = 1342.

3. Take the square root: r = √17956 = 2 × 67 = 134.

So there are 134 trees in each row.

Cross-check

Multiply back: 134 × 134 = 1342 = 17956, which matches the given total, confirming r = 134.