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36 x K is a perfect cube number, then K = ______
a)6
b)5
c)4
d)3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
36 x K is a perfect cube number, then K = ______a)6b)5c)4d)3Correct an...
6x6=36
6x6x6=216 which is a perfect cube
hence, the answer is 6.
6x6x6=216 which is a perfect cube
hence, the answer is 6.
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36 x K is a perfect cube number, then K = ______a)6b)5c)4d)3Correct an...
Solution:
If 36 x K is a perfect cube number, then it can be expressed as
36 x K = n^3, where n is a positive integer.
Breaking 36 into its prime factors, we get:
36 = 2^2 x 3^2
Substituting this in the above equation, we get:
2^2 x 3^2 x K = n^3
Simplifying the equation, we get:
K = (n/6)^3
Therefore, K will be a perfect cube number only if n is a multiple of 6.
Hence, the only option that satisfies this condition is option 'A' i.e., K = 6.
If 36 x K is a perfect cube number, then it can be expressed as
36 x K = n^3, where n is a positive integer.
Breaking 36 into its prime factors, we get:
36 = 2^2 x 3^2
Substituting this in the above equation, we get:
2^2 x 3^2 x K = n^3
Simplifying the equation, we get:
K = (n/6)^3
Therefore, K will be a perfect cube number only if n is a multiple of 6.
Hence, the only option that satisfies this condition is option 'A' i.e., K = 6.
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36 x K is a perfect cube number, then K = ______a)6b)5c)4d)3Correct answer is option 'A'. Can you explain this answer?
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