Determine the perfect cube whole number closest to 205 632

 205,209

Step-by-step explanation:

We want to find a perfect cube that is closest to the number N = 205,632

A perfect cube number is a number such that the square root is a whole number.

Now, to search this number we must take the square root of N:

n = √(205,632) = 453.47

Now, we can round it down or up and get whole numbers, and the squares of those whole numbers will be perfect squares that are near 205,632, lets start with rounding down.

n = 453

the square of 453 is:

453^2 = 205,209

If instead we round up the  453,47, we would get:

n = 454

and the square will be

n = 454^2 = 206,116

Now, to see which one is closser to N, we can take the differences:

205,632 -  205,209 = 423

206,116 - 205,632 = 484

so if we take n = 453 we are closser no N, then the perfect square that is closest to 205,632 is 205,209

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