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!
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.
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.
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