Presentation on theme: "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."— Presentation transcript:
1 SurdsAn Irrational Number is a real number that cannot be written as a simple fraction.Irrational means not RationalExample: 1.5 is rational, because it can be written as the ratio 3/2Example: 7 is rational, because it can be written as the ratio 7/1Example (3 repeating) is also rational, because it can be written as the ratio 1/3
4 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 surdExample: √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")
5 Surds Surds are square roots that can’t be written as a whole number. is not a surd, as it can be written as 57 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.
6 𝒂𝒃 = 𝒂 𝒃 Simplify 12 + 2 27 = 4 3 + 2 9 3 = 2 3 + 6 3 Example 1: 𝒂𝒃 = 𝒂 𝒃This 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 ===