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Algebra: Simplifying Surds
Without evaluating square roots as decimals, simplify
3 + √5
---
2 – √5
 = + √5

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Worked Solution:

Rationalise the denominator by multipling both numerator and denominator by 2 + √5:
3 + √5
---
2 – √5
 =
(3 + √5)(2 + √5)
---
(2 – √5)(2 + √5)
 =
6 + 3 √5 + 2 √5 + √52
---
4 – √52
 =
11 + 5 √5
---
–1
 = –11–5 √5

© MEI Produced by Dr Ron Knott, 21 July 2004
tom . button [AT] mei . org . uk 		Test reference: AlgSurdSimp.html?ref=83352