Millburn Academy Maths department National 5 Surds 1.

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Presentation transcript:

Millburn Academy Maths department National 5 Surds 1

A surd is an irrational number, which is the root (square, cube etc) of another number. Examples: 2 = 1∙414213562…. so 2 is a surd 3 = 1∙732050808…. so 3 is a surd 4 = 2 so 4 is NOT a surd 3 5 = 1∙709975947…. so 3 5 is a surd

We can add or subtract surds of the same value. Examples: 3 + 3 = 2× 3 or 2 3 5 2 +4 2 = 9 2 10 7 −6 7 = 4 7 12 5 +4 5 −6 5 = 10 5

Simplifying Surds 8 is a surd but it can be simplified We can simplify a surd if it can be divided by a square number. Reminder: Square Numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 …. 8 = 4 × 2 =2 × 2 =2 2

Simplifying the following surds: 1) 45 = 9 × 5 3) 80 = 16 × 5 =3 5 =4 5 2) 75 = 25 × 3 4) 700 = 100 × 7 =5 3 =10 7

These surds are different so can’t be added together. 5) 3 + 12 = 3 + 4 3 However 12 can be simplified. = 3 +2 3 =3 3 We can now add them together. 6) 98 − 32 = 49 × 2 − 16 × 2 =7 2 −4 2 =3 2