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Algebra: Simplifying Surds
Without evaluating square roots as decimals, simplify
3 + √2
---
4 + √2
 = + √2

tickcross


Worked Solution:

Rationalise the denominator by multipling both numerator and denominator by 4 – √2:
3 + √2
---
4 + √2
 =
(3 + √2)(4 – √2)
---
(4 + √2)(4 – √2)
 =
12 – 3 √2 + 4 √2 – √22
---
16 – √22
 =
10 + √2
---
14
 =
5
---
7
 +
1
---
14
 √2

© MEI Produced by Dr Ron Knott, 21 July 2004
tom . button [AT] mei . org . uk 		Test reference: AlgSurdSimp.html?ref=28325,qu=div