Q: Perfect squares less than 101

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1,4,9,16,25,36,49,64,81,100

The sum of the first positive odd integers less than 101 is 10,000.

101 and 26

NON perfect squares are just regular # that aren't squares: 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42 ,43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56 , 57 ,58, 59, 60, ,61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75 ,76, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101,... (skipping 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, because they ARE perfect squares of numbers)

4 rectangles. (I'm assuming you mean 1414 congruent squares) Suppose we made a rectangle out of 1414 squares. Then its area is 1414x2, if x is the length of a square's side, and all its sides are multiples of x. Say the length and width are ax and bx, then we have two ways of finding the area, which must be equal: ax*bx=1414x2, or ab=1414. Now we just need to find the number of ways to get 1414 as a product of two whole numbers. 1414 factors as 2*7*101 (which are all prime), so there are 4 ways to split it up: 1414 = 1*1414 = 2*707 = 7 * 202 = 14 * 101. Each of these ways gives a different rectangle made up of 1414 squares.

Related questions

The perfect squares less than 101 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

1,4,9,16,25,36,49,64,81,100

The perfect squares less than 101 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

101 is aprime number....

101

101

12= 1 22= 4 32= 9 42= 16 52= 25 62= 36 72= 49 82= 64 92= 81 102= 100

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

101 is greater by two orders of magnitude.

It is: 101-5 = 96

The sum of the first positive odd integers less than 101 is 10,000.