### 6AM Quiz (2011, 16 July): Huge numbers are not big deal!

Which number is larger:
(987 654 324)^2
or
(987 654 320) x (987 654 328) ?

1. (987 654 324)^2 is larger than (987 654 320) x (987 654 328). It is so, the only difference is the last number.

So we will ignore the first 8 numbers, so (4)^2=8, while 0x8=0#

2. @Leighton

Good attempt :)

Would you be able to use algebra to explain you answers?

3. Erm...987654320 x 987654328 is larger cos' the difference between 987654324 and itself (zero) to the power of 2 is smaller than the difference between 987654320 and 987654328 (8) to the power of 2.

4. Both are equal. This question is just like the first question in the "supervised study" paper.

5. This comment has been removed by the author.

6. (987 654 324)^2 and (987 654 320) x (987 654 328) has the same starting eight numbers. So to determine which is bigger, it is relies on the last number which is different. However, this is not certain as the numbers go higher example: 24^2 to 28 x 20, the numbers change and become different, so it varies. This means that their equal.

Another side of the story is that 4x4 = 16, and 8 x 0 = 0. This means that (987 654 324)^2 is bigger than (987 654 320) x (987 654 328).

So Confusing o.O

7. (987654324)^2 is larger than (987654320)x(987654328).

Erm.as...(987654324)^2 would equal to
(987654324)(987654324)

While...(987654320)x(987654328)
=(987654320)(987654328)

So we shall compare the difference of these 2 numbers, as the difference of only the last number is the only difference, we shall ignore the rest of the first 8 numbers.

So it would be (4)^2 to 0x8
=8 to 0
So this shows that (987654324)^2 is larger than (987654320)x(987654328).

8. (987654324)^2=(987654324)(987654324)

As the front 8 numbers which are, 98765432, are the same, only the last number is different.

The difference:
(4)^2 compared to 0x8
which is
4x4 to 0x8
= 16 to 0

Hence, that proves that (987654324)^2 is larger than (987654320)(987654328).

9. The front of the numbers are all the same, so only the products of the last numbers are essential. Since 4^2 is 8, while 8x0 is 0, therefore, (987 654 324)^2 is bigger than (987 654 320) x (987 654 328) .

10. @Mitsunari Ishida (er... u are???):
Elaborate further, perhaps some kind of mathematical statements will help us to understand better?

@Ben:
Would it be easier if you try to give one more example to illustrate your point? Hm... Possible to use Algebra to explain?

@Ryan Yeo:
To compare, can we just drop the numbers in front of it and make comparison? Does that work all the time?

@Amelia:
Can we just compare the numbers in this manner? How to support what you say works for all instances?

@Luke:
Same question as I ask the rest... how to justify what you explained for all cases? Would algebra help to explain the difference better?

11. let 987654324 be x.
Which is bigger? x^2 or (x-4)*(x+4)=x^2-16
x^2 is bigger so the answer is 987654324

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13. let 98754320 be X

(987654324)^2
= (X+4)^2
= (X)^2 + 2(X)(4) + (4)^2
= X^2 + 8X +16

(987654320) x (987654328)
= (X)(X+8)
=X^2 +8X

(987654324)^2 > (987654320) x (987654328)

14. @Joshua @Siddharth

While both of you use a different x value, hence resuming a different set of working, both of you have explained very clearly to support your conclusion.

Well done :)