Question

Find the largest 4 digit number which is a perfect cube

Answer 1

Solution :-

The largest 4 digit number is 9999. But 9999 is not a perfect cube. 

The largest 4 digit perfect cube number can be obtained by cubing some natural numbers at random. 

⇒ 10*10*10 = 1000 - which is very much less than the largest 4 digit number, which is 9999.

⇒ 15*15*15 = 3375 - It is also very much less than the largest 4 digit number, which is 9999.

⇒ 20*20*20 = 8000 - It is also less than the largest 4 digit number, which is 9999.

⇒ 21*21*21 = 9261 - It is also less than the largest 4 digit number, which is 9999.

⇒ 22*22*22 = 10648 - It is greater than the largest 4 digit number, which is 9999.

So, we can conclude that 9261 is the largest 4 digit perfect cube number, which is the cube of 21.

Answer.

Answer 2

The largest 4 digit number = 9999.

Let us take some Numbers to obtain cube


10³ = 1000 it is less than largest 4-digit number


16³ = 4096 it is less than largest 4-digit number


20³ = 8000 it is less than largest 4-digit number

21³= 9261 which is less than largest 4-digit number

22³ = 10648 it is greater than largest 4-digit number (9999).


Hence, we can observe that 9261 is the largest 4-digit perfect cube.

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Hope this will help you...