Technically 0, 9 and 16 qualify. Add any two together and they still make perfect squares (i.e. numbers whose square roots are integers).
I couldn't find any others < 625 or 252
41, 80 and 320 work!
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Also, 17, 32, and 32
and 72, 72, and 217
...
There is no limit to the number of perfect squares. To find a perfect square, you simply need to pick a number and square it. E.g. 7^2=49, so 49 is a perfect square. As there is infinitely many numbers to pick, and as the larger a number the larger it's square, there are infinitely many perfect squares and they just keep on getting larger!
If its square root can be expressed as a rational number then it is a perfect square. 9075 is not a perfect square. However, 9025 is.
You can. Just add the numbers together, and find their square root. One plus three is four; the square root of the sum is two.
create a program that iterates until it finds a perfect number, then store that perfect number into an array. Continue iterating until you find three more. Then, you have an array of four perfect numbers.
say u have the number 16. Its square root is 4. the square root(4) is the number that, when multiplied by itself, gives the original number (16). To find a square root you must first find the two closet perfect squares (a square being the product of a square root, a perfect square being the product of square roots that are whole numbers 1,2,3,4, ect.) then u find the approxomate distance between
sqrt(30)= 5.5 approx sqrt(40) = 6.3 approx The integer 6 is between the square roots. So the square of 6, which is a perfect square, will be between the two original numbers. So answer is 62 = 36.
Because numbers are infinite, there is an infinite number of answers. e.g. What number should be added to 2 to make a perfect square? 2+2=4 (a perfect square) 2+7=9 (a perfect square) 2+14=16 (a perfect square) 2+23=25 (a perfect square) etc... Did you have a specific number in mind.
-20
5607 + 18 = 5625, a perfect square. The perfect square of a square root is the number you started with.
To find a number that is both a perfect square and a perfect cube, we must solve x2 = x3 over x ∈Z+. The only two solutions to this equation are 0 and 1, or x = {0,1}. Therefore, zero and one are the only two numbers that are both perfect squares and perfect cubes. --In easier terms: a perfect square is a number that can be "square rooted" and have no remainder. Like, 144. The square root is 12 therefore 144 is a perfect square. A perfect Cube is the same except that it must be "cubed rooted". Like 27. The cube root of this number is 3 therefore 27 is a perfect cube.
12, 13 and 14
14, 15, 16