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Surds An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational Example: 1.5 is rational, because it can be written as the ratio 3/2 Example: 7 is rational, because it can be written as the ratio 7/1 Example (3 repeating) is also rational, because it can be written as the ratio 1/3

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**How did we get the word "Surd" ?**

If you can't simplify a number to remove a square root (or cube root etc) then it is a surd. Example: √2 (square root of 2) can't be simplified further so it is a surd Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd! In fact "Surd" used to be another name for "Irrational", but it is now used for a root that is irrational. How did we get the word "Surd" ? Well around 820 AD al-Khwarizmi (the Persian guy who we get the name "Algorithm" from) called irrational numbers "'inaudible" ... this was later translated to the Latin surdus ("deaf" or "mute")

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**Surds Surds are square roots that can’t be written as a whole number.**

is not a surd, as it can be written as 5 7 is a surd, as it can’t be written as a whole number. There are rules that we can follow that will allow us to simplify a surd as much as possible.

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**𝒂𝒃 = 𝒂 𝒃 Simplify 12 + 2 27 = 4 3 + 2 9 3 = 2 3 + 6 3 Example 1:**

𝒂𝒃 = 𝒂 𝒃 This rule helps us simplify surds by splitting the surd into a surd and a non-surd The non-surd can then be simplified into a whole number. Example 1: Simplify = = =

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**𝒂 𝒃 = 𝒂 𝒃 Simplify 44 11 + 25 36 = 44 11 + 25 36 = 4 + 5 6 = 2 + 5 6**

𝒂 𝒃 = 𝒂 𝒃 Example 2: Simplify = = = =

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