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By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?
- a)2
- b)14
- c)7
- d)49
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
By which smallest natural number 392 must be multiplied so as to make ...
392 = 2 × 2 × 2 × 7 × 7
Hence the number should be multiplied by 7 to make it a perfect cube.
Most Upvoted Answer
By which smallest natural number 392 must be multiplied so as to make ...
392 = 2 X 196
= 2 X 2 X 98
= 2 X 2 X 2 X 49
= 2 X 2 X 2 X 7 X 7
Thus 392 is not a perfect cube.
To make it a perfect cube multiply 392 with 7.
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Community Answer
By which smallest natural number 392 must be multiplied so as to make ...
Explanation:
Finding the Smallest Natural Number:
To find the smallest natural number by which 392 must be multiplied to make the product a perfect cube, you need to factorize 392 into its prime factors.
Prime Factorization of 392:
392 = 2^3 * 7^2
Determining the Missing Factors:
For the product to become a perfect cube, each prime factor in the prime factorization must occur in groups of three. Looking at the prime factorization of 392, we can see that 2 is missing a factor to make it a perfect cube.
Finding the Missing Factor:
To find the missing factor, we need to calculate the cube root of 392, which is approximately 7.14. Since 7 is a factor in the prime factorization of 392, we need to multiply 392 by 7 to make it a perfect cube.
Calculating the Missing Factor:
392 * 7 = 2744
Verification:
Now, the prime factorization of 2744 is 2^3 * 7^3, which is a perfect cube.
Therefore, the smallest natural number by which 392 must be multiplied to make the product a perfect cube is 7.
Finding the Smallest Natural Number:
To find the smallest natural number by which 392 must be multiplied to make the product a perfect cube, you need to factorize 392 into its prime factors.
Prime Factorization of 392:
392 = 2^3 * 7^2
Determining the Missing Factors:
For the product to become a perfect cube, each prime factor in the prime factorization must occur in groups of three. Looking at the prime factorization of 392, we can see that 2 is missing a factor to make it a perfect cube.
Finding the Missing Factor:
To find the missing factor, we need to calculate the cube root of 392, which is approximately 7.14. Since 7 is a factor in the prime factorization of 392, we need to multiply 392 by 7 to make it a perfect cube.
Calculating the Missing Factor:
392 * 7 = 2744
Verification:
Now, the prime factorization of 2744 is 2^3 * 7^3, which is a perfect cube.
Therefore, the smallest natural number by which 392 must be multiplied to make the product a perfect cube is 7.
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By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?a)2 b)14c)7 d)49Correct 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 By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?a)2 b)14c)7 d)49Correct 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 By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?a)2 b)14c)7 d)49Correct answer is option 'C'. Can you explain this answer?.
By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?a)2 b)14c)7 d)49Correct 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 By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?a)2 b)14c)7 d)49Correct 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 By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?a)2 b)14c)7 d)49Correct answer is option 'C'. Can you explain this answer?.
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