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Algebra: Simplifying Surds
Without converting surds to decimals, simplify
( –1 – 2 √6)3 = + √6

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Worked Solution:

Either use the Binomial Theorem or multiply out 3 copies of the bracketed term:
( –1 – 2 √6)3
= ( –2 √6)3 + 3 (–1) ( –2 √6)2 + 3 (–1)2(–2)√6 + (–1)3
= –8 √63 – 12 √62 – 6 √6 – 1
= –73 – 54 √6

© MEI Produced by Dr Ron Knott, 21 July 2004
tom . button [AT] mei . org . uk 		Test reference: AlgSurdSimp.html?ref=31486,qu=pow