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Perfect squares less than 101

Updated: 4/28/2022
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Integers which are the squares of integers are called perfect squares or square numbers.

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

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Q: Perfect squares less than 101
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What are all the perfect squares less than 101?

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


What is the sum of the first positive odd integers less than 101?

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


The difference of two numbers is 75. The larger number is three less than four times the smaller number. Find the numbers.?

101 and 26


What are some examples of NON perfect squares?

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)


How many rectangles can be made from 1414 squares?

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.