Find the greatest number of seven digits which is a perfect square.

Find the least number which is a square and exactly divisible by each of the numbers $8, 12, 15, \text{and} 20$.

Find the least number that must be added to $506900$ to make it a perfect square. Find the perfect square and its square root.

The cost of levelling and turfing a square lawn at $₹2.50$ per square metre is $₹13322.50$. Find the cost of fencing it at $₹5$ per metre.

The area of a square field is $60025 {\mathrm{m}}^2$. A man cycles along its boundary at $18 \mathrm{km}/\mathrm{hr}$. In how many hours will he return to the starting point.