operations with surds

Similar or like surds are surds with the same radicand and index.

Addition or subtraction: You can only add or subtract similar or like surds:

√2 + 3√2 = 4√2

√5+√3 = √5+√3

√7-15√7 = -14√7

Multiplication and division: If the surds have the same index, you can do as follows:

√2 · √3 = √6 

If they don’t have the same indices, we have to look for equivalent surds with the same index, using the LCM:

 

Powers:

 

Exercise: calculate:

a)√12-3√3+2√75=

b) 3√54-3√16+3√250=

c) √3·3√9·4√27=

d) √256:3√16=

e) (√a·3√a2·4√a3)/6√a4=

 

 

 

Solutions: a) 9√3; b) 63√2; c) 3·12√311; d) 4·3√4; e) 4√a5; f) 24√217

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