Powers, roots and logarithms

# 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}√a^{2}·^{4}√a^{3})/^{6}√a^{4}=

Solutions: a) 9√3; b) 6^{3}√2; c) 3·^{12}√3^{11}; d) 4·^{3}√4; e) ^{4}√a^{5}; f) ^{24}√2^{17}

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