**Question**

**Introduction**

To the Chinese,
the number 8 (八) is considered to be auspicious, because it
sounds like “prosper” (发) in the various Chinese
languages/dialects. But the LHS expression
featured above seems too prosperous for comfort. There is an explosion of 8s
coupled with eighth roots. How to
even handle that?

**Strategy**

As usual,
often one good tactic is to

*look for patterns*or*chunks*. [H04] Can you see the sub-expressions containing the eighth roots (highlighted in green and pink)?
Do you notice any similarities between the two chunks?
Do you notice any difference(s)?

If we call the green chunk

*a*and the pink chunk*b*, we can remove the roots by taking the eighth powers. Then we get whole numbers, which are less complicated.**Solution**

**Remark**

The crux of the problem is the factorisation
of

For another example of using the difference of squares formula, please look at thisarticle.

*a*^{8}–*b*^{8}. It is based on repeated application of the difference of squares*X*^{2}–*Y*^{2}= (*X*+*Y*) (*X*–*Y*) formula which schools expect students to know.For another example of using the difference of squares formula, please look at thisarticle.

H04. Look for
pattern(s)

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

*****“IP Mathematics” so called

* challenge for students taking GCE ‘O’ Level Additional Mathematics

* other syllabuses that involve surds

* precocious kids who like to test themselves

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