How to find square in fast way

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A square is drawn by joining the mid-points of the sides of a square. A third square is drawn inside the second square in the same way and the processes continued indefinitely. If the side of the square is 10 c m , find the sum of the areas of all the squares so formed.

A square is drawn by joining mid pint of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued in definitely. If the side of the first square is 16 cm, then what is the sum of the areas of all the squares ?

Find the square of : 59

Find the square of : 15

Find the square of: 2a +b

Find the number of ways in which we can choose 3 squares on a chess board such that one of the squares has its two sides common to other two squares.

Is 2352 a perfect square? if no, find the smallest multiple of 2352 which is a perfect square. also find the square root of the new number?

Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square.