36 is the square of 6; 100 is the square of 10; 121 is the square of 11. 71, 62, and 343 are not squares of whole numbers.
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A trick for figuring out squares of larger numbers that is sometimes helpful: if you can write the numbers as the product of two different numbers, then you can square those two numbers and multiply that to find the square of the original. 602 = 102*62 = 100*36 = 3600
18 times
The digit 3 will be written 20 times.
Among the whole numbers, these are:149162536496481100
100,000,000,000,000