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Algebra: Simplifying Surds
Without evaluating square roots as decimals, simplify
–3 – √2
---
–1 – √2
 = + √2

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Worked Solution:

Rationalise the denominator by multipling both numerator and denominator by –1 + √2:
–3 – √2
---
–1 – √2
 =
( –3 – √2)( –1 + √2)
---
( –1 – √2)( –1 + √2)
 =
3 – 3 √2 + √2 – √22
---
1 – √22
 =
1 – 2 √2
---
–1
 = –1 + 2 √2

© MEI Produced by Dr Ron Knott, 21 July 2004
tom . button [AT] mei . org . uk 		Test reference: AlgSurdSimp.html?ref=75235,qu=div