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What is smallest number with which 5400 may be multiplied so that the product is perfect cube?
- a)5
- b)3
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is smallest number with which 5400 may be multiplied so that the ...
∛(5400 x 5) = 30
Most Upvoted Answer
What is smallest number with which 5400 may be multiplied so that the ...
Just use the prime factorisation method.
Find the factors of 5400
They are 2³×3³×5²
So in order to get a perfect cube 5 must be multiplied.
CROSS CHECK
5400×5=27000
And 27000 is cube of 30...
Hence yur answer will be 5...
Find the factors of 5400
They are 2³×3³×5²
So in order to get a perfect cube 5 must be multiplied.
CROSS CHECK
5400×5=27000
And 27000 is cube of 30...
Hence yur answer will be 5...
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What is smallest number with which 5400 may be multiplied so that the ...
Smallest Number to Multiply with 5400 to Make it a Perfect Cube
To find the smallest number with which 5400 may be multiplied so that the product is a perfect cube, we need to follow the below steps:
Step 1: Prime Factorization of 5400
We need to find the prime factorization of 5400 to determine the smallest number with which it can be multiplied to make it a perfect cube.
5400 = 2^3 × 3^3 × 5^2
Step 2: Find the Missing Prime Factors
To make 5400 a perfect cube, we need to multiply it by some number that contains the missing prime factors. The missing prime factors in 5400 are 2 and 5. Therefore, we need to multiply 5400 with 2 × 5 = 10.
Step 3: Check if the Product is a Perfect Cube
Now, we need to check if the product of 5400 and 10 is a perfect cube or not.
5400 × 10 = 2^4 × 3^3 × 5^3
The product is a perfect cube as all the exponents of the prime factors are divisible by 3.
Step 4: Determine the Smallest Number
As we have found that multiplying 5400 by 10 makes it a perfect cube, we can conclude that the smallest number with which 5400 may be multiplied so that the product is a perfect cube is 10.
Therefore, the correct answer is option 'A' i.e. 5 is the smallest number with which 5400 may be multiplied so that the product is a perfect cube.
To find the smallest number with which 5400 may be multiplied so that the product is a perfect cube, we need to follow the below steps:
Step 1: Prime Factorization of 5400
We need to find the prime factorization of 5400 to determine the smallest number with which it can be multiplied to make it a perfect cube.
5400 = 2^3 × 3^3 × 5^2
Step 2: Find the Missing Prime Factors
To make 5400 a perfect cube, we need to multiply it by some number that contains the missing prime factors. The missing prime factors in 5400 are 2 and 5. Therefore, we need to multiply 5400 with 2 × 5 = 10.
Step 3: Check if the Product is a Perfect Cube
Now, we need to check if the product of 5400 and 10 is a perfect cube or not.
5400 × 10 = 2^4 × 3^3 × 5^3
The product is a perfect cube as all the exponents of the prime factors are divisible by 3.
Step 4: Determine the Smallest Number
As we have found that multiplying 5400 by 10 makes it a perfect cube, we can conclude that the smallest number with which 5400 may be multiplied so that the product is a perfect cube is 10.
Therefore, the correct answer is option 'A' i.e. 5 is the smallest number with which 5400 may be multiplied so that the product is a perfect cube.
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What is smallest number with which 5400 may be multiplied so that the product is perfect cube?a)5b)3c)4d)6Correct answer is option 'A'. Can you explain this answer?
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What is smallest number with which 5400 may be multiplied so that the product is perfect cube?a)5b)3c)4d)6Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about What is smallest number with which 5400 may be multiplied so that the product is perfect cube?a)5b)3c)4d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is smallest number with which 5400 may be multiplied so that the product is perfect cube?a)5b)3c)4d)6Correct answer is option 'A'. Can you explain this answer?.
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