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What is the smallest positive integer which you can multiply to 5688 to make it a perfect square?
In the prime factorisation of a perfect square in power format, all primes must be to an even power.
5688 = 23 x 32 x 79
To convert this it a perfect square, it needs the 2 and 79 to have an even power - the 3 is already at an even power.
The smallest way to do this is to multiply 5688 by 2 x 79, ie multiply it by 158.
5688 x 158 = 23 x 32 x 79 x 2 x 79
= 24 x 32 x 792
= (22 x 3 x 79)2
= (948)2
= 898704
What else can I help you with?
What is the smallest positive integer that has exactly 6 perfect square divisors?
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Perfect squares are positive. A smallest negative number doesn't exist. The four smallest prime numbers are 2, 3, 5 and 7. The smallest perfect square would have to be 2^2 x 3^2 x 5^2 x 7^2 or 44,100
Product of an integer multiplied by itself?
perfect square
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A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.Integers are rational numbers so the square [which is an integer] is a rational number.
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