**Question**

**Introduction**

**are expressions involving roots like square roots. They are usually**

*Surds***numbers. If you try to put them into a**

*irrational***of integers, you are**

*ratio***! Many students (and teachers?) are not sure of how to put square roots of numbers in a simple form. The trick is to use**

*absurd**square numbers*or

**. These are squares of whole numbers. For example:-**

*perfect squares*
1

^{2}= 1 ´ 1 = 1 Ö1 = 1
2

^{2}= 2 ´ 2 = 4 Ö4 = 2
3

^{2}= 3 ´ 3 = 9 Ö9 = 3
4

^{2}= 4 ´ 4 = 16 Ö16 = 4
5

^{2}= 5 ´ 5 = 25 Ö25 = 5
A number like 4
can be represented by a real square
whose sides have length 2 units.
Note also that if you take the square root of a perfect square, you
always get a nice whole number.

How do you
deal with numbers that are not perfect squares? You factor out as many perfect squares as
possible. This would eventually lead to surds
with small numbers, which are more manageable.
Here are some examples:-

With this weapon in our hands, let us kick some butt.

**Solution**

**Moral of the Story**

Using
perfect squares reduces your square roots to surds involving square roots of
prime numbers, which are easier to combine or cancel. This gives a short and sweet solution. In mathematics, always try to do things by
the cleanest way (if you can).

H10. Simplify
the problem

H11. Solve part
of the problem

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

* revision for GCE ‘A’ Level H2 Mathematics

* revision for IB Mathematics HL / SL

* other syllabuses that involve surds

* precocious kids who always want to learn more

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