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True. By definition, a Prime number is divisible by one and by itself. Also by definition, a perfect square has at least an additional pair of factors - it's square root. Therefore a prime number could never be a perfect square.
One exception that might come to mind in this case is the number one. One however, is not considered a prime number, and thus does not conflict with this rule.
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Can a prime number be a perfect square?
No.
Will the square root of a prime number be rational or irrational?
Nice question! The square root of (any number that isn't a perfect square) is irrational. No prime number is a perfect square. So the square root of any prime number is irrational.
Is a prime number cannot be a perfect square?
That is correct.
Which outcome is least likely to occur on a single spin 1 an odd number 2 a prime number 3 a perfect square 4 a number divisible by 2?
a perfect square
What is the sum of the fifth prime number the sixth composite number and the third perfect square?
11 + 12 + 9 = 32
Can a prime number be a perfect square?
No.
Will the square root of a prime number be rational or irrational?
Nice question! The square root of (any number that isn't a perfect square) is irrational. No prime number is a perfect square. So the square root of any prime number is irrational.
Is 1 a prime number or a square number?
1 is not considered a prime number; 1 is a perfect square.
Can a perfect square be a prime number Explain?
No. A prime number is always odd.
Is there a prime number where there is 1 less than a perfect square?
3 is prime, 1 less than the perfect square of 4 (2x2)
What number is a perfect square the only prime number in its prime factorization is 2 and the sum is odd?
16
Why is the number 40 not a perfect square?
because it needs to be a prime number and it has to be simplified
Is there a product of two perfect squares that is not a perfect square?
No there isn't. every perfect square number can be factored into prime number. At their factoration you'll always have multiples of two on the primes exponent. Therefore you'll multiply a prime raised to a 2-multiple number with another prime raised to a 2-multiple number wich gives you also a number that factored gives you a product of prime numbers raised to a 2-multiple number and so, a perfect square.
Is 5329 a prime number?
No, it's a perfect square 73 * 73.
Is a prime number cannot be a perfect square?
That is correct.
If a number has an odd number of factors is it a perfect square?
If you mean 'prime' factors, then an odd number of them CAN'T produce a perfect square. Consider 3 factors ... A, B, and C. If their product were a perfect square, then AxB=C, which can't be true if C is a prime number. For non-prime factors, an odd number of them may or may not be a perfect square: Three factors = not a square: 2 x 3 x 5 = 30. Three factors = a square: 2 x 3 x 6 = 36.
What number is a perfect square with 2 as its only prime number in its prime factorization?
4, 16, 64 and many others
