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Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.
- a)3
- b)9
- c)4
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Find the smallest number by which 54 must be multiplied so that the pr...
U know that 54=3^3*2^1,so to get a perfect cube we have to multiply it with 2^2 i.e 4.Hence option c is correct.....
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Find the smallest number by which 54 must be multiplied so that the pr...
Solution:
To find the smallest number by which 54 must be multiplied so that the product is a perfect cube, we need to express 54 as a product of its prime factors.
54 = 2 x 3 x 3 x 3
Now, to make the product a perfect cube, we need to multiply 54 by some number such that all the prime factors have an even power. Since the power of 2 in the prime factorization of 54 is already even, we only need to multiply by a number that will make the power of 3 even.
Therefore, the smallest number by which 54 must be multiplied so that the product is a perfect cube is 3 x 3 = 9.
Hence, the correct answer is option C.
Summary:
- Express 54 as a product of its prime factors: 54 = 2 x 3 x 3 x 3
- To make the product a perfect cube, we need to multiply by a number that will make the power of 3 even.
- The smallest number by which 54 must be multiplied so that the product is a perfect cube is 3 x 3 = 9.
- Therefore, the correct answer is option C.
To find the smallest number by which 54 must be multiplied so that the product is a perfect cube, we need to express 54 as a product of its prime factors.
54 = 2 x 3 x 3 x 3
Now, to make the product a perfect cube, we need to multiply 54 by some number such that all the prime factors have an even power. Since the power of 2 in the prime factorization of 54 is already even, we only need to multiply by a number that will make the power of 3 even.
Therefore, the smallest number by which 54 must be multiplied so that the product is a perfect cube is 3 x 3 = 9.
Hence, the correct answer is option C.
Summary:
- Express 54 as a product of its prime factors: 54 = 2 x 3 x 3 x 3
- To make the product a perfect cube, we need to multiply by a number that will make the power of 3 even.
- The smallest number by which 54 must be multiplied so that the product is a perfect cube is 3 x 3 = 9.
- Therefore, the correct answer is option C.
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Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.a)3b)9c)4d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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