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Which integer between 2 and 200000000000000 is a perfect square a perfect cube and a perfect fifth power?
Wiki User
∙ 14y ago
If a number is a perfect square, then its prime factors can be split into two identical groups: if a perfect cube, three groups; if a perfect fifth power, five groups. The best way to attain this sort of 'symmetry' is to only use one prime factor. Since we are looking for small (ish) solutions, we'll use 2. It only remains to decide how many 2's to multiply together. The number needs to be divisible by 2, 3 and 5. We are looking for the lowest common denominator of 2, 3 and 5, which is 30. 22x3x5 = 230 = 1073741824 = (22x3)5 = (22x5)3 = (23x5)2 The next smallest solution is given by 330 = 205891132094649, which is just a little bit bigger than 2 x 1014. So the question is correct in assuming that only one answer exists.
Wiki User
∙ 14y ago
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A perfect square is a number that has an integer square root?
Yes, a perfect square is a number that has an integer square root.
Is 300 perfect square root?
Any integer is a perfect square oot (of its square). So 300 is a perfect square root of 90000.
Is 111 a perfect square?
Since no integer multiplied by itself can yield 111, it is not a perfect square. 121, however, is a perfect square. Its square root is 11.
How are square roots and perfect squares related?
The square root of every perfect square is an integer. However, there are also square roots of numbers that are not perfect squares.
What is perfect square definition and example?
A perfect square is the square of an integer. For example, 1 (which is 12), 4 (22) or 9 (32) etc...
The square root of a perfect square is an integer?
Yes it is.Since the square of an integer is called a perfect square, then the square root of a perfect square must be an integer.
What is a perfect square?
A perfect square is a square of an integer (a whole number).
The square root of a perfect square and the cube root of a perfect cube is?
an integer
What is the smallest integer where the integer before it is a perfect square and the integer after it is a perfect cube?
The integer is 26
A perfect square is a number that has an integer square root?
Yes, a perfect square is a number that has an integer square root.
Given the prime factorization of an integer how can you determine if our integer is a perfect square?
Given the prime factorization of an integer how can you determine if our integer is a perfect square?
Is this integer 90 a perfect square?
90 is a not perfect square.
What is the definition of a non perfect square?
I have never before heard of a non-perfect square but I suppose it would be any non-zero number that is not the square of an integer. People sometimes say "perfect square" to mean an integer that is a square of an integer - I think the "perfect" is redundant but if you do not think "square" is clear by itself, say "integer square."
Has an integer as its square root?
A perfect square.
What has an integer as its square roots?
a perfect square
What is a square of an integer called?
A perfect square.
Why are perfect square and cube perfect?
Because they are square/cube of an integer.
