
The smallest number by which 3600 can be divided to make it a perfect cube is:
A. 9
B. 50
C. 300
D. 450
Answer
490.5k+ views
Hint: A perfect cube is an integer which is equal to another integer raised to the power 3. For example 125 is a perfect cube as it can be written as , 5 raised to the power 3. So divide 3600 by every given option and if the result obtained can be written as a perfect cube then that particular option is our answer.
Complete step-by-step answer:
We are given to determine the smallest number by which 3600 can be divided to make it a perfect cube.
First one is 9, when 3600 is divided by 9 we get . But 400 is a perfect square of 20 but not a perfect cube.
Second one is 50, when 3600 is divided by 50 we get . 72 cannot be written as a perfect cube.
Third one is 300, when 3600 is divided by 300 we get . 12 is not a perfect cube.
Fourth one is 450, when 3600 is divided by 450 we get . 8 can also be written as 2 raised to the power 3.
This means that 8 is a perfect cube of 2. So 3600 must be divided by 450 to make it a perfect cube
So, the correct answer is “Option D”.
Note: Another approach
First we have to factorize 3600.
3600 can also be written
As we can see in the prime factorization of 3600, there is a repeated factor 2 for four times and remaining factors are repeated less than 3 times.
For a perfect cube there must be a repeating factor for 3 times.
So 3600 must be divided by to give a perfect cube
And
So 3600 must be divided by 450 to give a perfect cube 8.
Complete step-by-step answer:
We are given to determine the smallest number by which 3600 can be divided to make it a perfect cube.
First one is 9, when 3600 is divided by 9 we get
Second one is 50, when 3600 is divided by 50 we get
Third one is 300, when 3600 is divided by 300 we get
Fourth one is 450, when 3600 is divided by 450 we get
This means that 8 is a perfect cube of 2. So 3600 must be divided by 450 to make it a perfect cube
So, the correct answer is “Option D”.
Note: Another approach
First we have to factorize 3600.
3600 can also be written
As we can see in the prime factorization of 3600, there is a repeated factor 2 for four times and remaining factors are repeated less than 3 times.
For a perfect cube there must be a repeating factor for 3 times.
So 3600 must be divided by
And
So 3600 must be divided by 450 to give a perfect cube 8.
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