Smallest number by which 2592 be multiplied so that the product is a perfect square
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We factor the given number, Show 2592 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 2592 = 36√2 We have to multiply 2 so that we get a perfect square. = 2592 x 2 = 5184 = √5184 = 72 Therefore, The smallest number is 2 which has to be multiplied. ← Prev Question Next Question → 0 votes 6.1k views asked Sep 15, 2018 in Mathematics by AnujPatel (53.9k points) Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
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answered Sep 15, 2018 by
SunilJakhar (89.6k points) Best answer On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor. ← Prev Question Next Question → Find MCQs & Mock Test
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... What is the smallest number by which 2592 must be multiplied so that the product is a perfect cube?∴ The given number should be multiplied by 3187.
Is 2592 a perfect cube?Answer. so, multiplying bu 2*3^2 = 18 will make 2592 a perfect cube...
What is the prime factorization of 2592?Factors of 2592 are numbers that, when multiplied in pairs give the product as 2592. There are overall 30 factors of 2592 among which 2592 is the biggest factor and its prime factors are 2, 3. The Prime Factorization of 2592 is 25 × 34.
What is the smallest number by which 2592 must be divided so that the quotient is a perfect cube?Hence 2592 must be divided by 12 to make it a perfect cube.
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