How to find the largest 4 digit no. which is a perfect cube? pls help me fast and im getting prime factors as 3 x 3 x 11 x 101 . So can u pls help me with the next step. my exams r nearing.pls help me as fat as u can

Lalit Mehra , Meritnation Expert added an answer, on 7/9/11

Hi!

Here is the answer to your query.

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

Let’s take the number say 10.

10^{3} = 1000 which is very less than **largest** 4-digit number

Let’s now take 15.

15^{3} = 3375 which is still less than **largest** 4-digit number

Now let us take 20.

20^{3} = 8000

Now, let’s take 21.

21^{3} = 9261

Now take 22.

22^{3} = 10648 which is greater than **largest** 4-digit number (9999)

So, we can conclude that 9621 is the **largest** 4-digit perfect cube.

Cheers!

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