Question

A gardener has 36562 plants. He wants to arrange them in the form of a square with equal number of columns and rows. After arranging, he found some of the plants unused. The remaining plants are?

• A. 36
• B. 65
• C. 81
• D. 97

Hint:

Use the square root to find the closest perfect square for arranging items in square form and subtract to find leftovers.

Answer 1

The Correct Option is C

Step 1: Understanding the problem
The gardener wants to arrange the plants in a perfect square formation. This means the total number of plants arranged should be a perfect square (equal rows and columns). Some plants will be leftover if 36562 is not a perfect square.
Step 2: Find the closest perfect square less than 36562
Calculate the integer part of the square root of 36562:
\(\sqrt{36562} \approx 191.26\)
The closest perfect square less than 36562 is \(191^2\). Calculate:
\(191^2 = 191 \times 191 = 36481\)
Step 3: Calculate leftover plants
Leftover = Total plants - arranged plants
= 36562 - 36481 = 81
Step 4: Conclusion
So, 81 plants remain unused after arranging in square form.
Hence, Option (C) 81 is correct.