Download supplemental sheet #5

SUPPLEMENTAL SHEET #5
TOPIC: CONJUGATE SURDS, RATIONALISATION OF SURDS
Conjugate surds are specially related surds such as:
,
Their product is always a a rational number, as
The idea of conjugate surds is important for rationalizing the denominator.
Find the conjugate surds of:
1.
2.
3.
Solutions:
1.
2.
3.
The idea of rationalizing the denominator is to simplify a fraction such that
there are no surds in the denominator. This is done by multiplying the
numerator and denominator by the conjugate surd of the denominator.
Rationalizing the denominator is an important idea as it simplifies algebraic
manipulation, for example, in combining two fractions involving surds.
Simplify the following fractions:
this does not change the
=
magnitude of the expression as it
is essentially multiplying by 1
=
=
=
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Taken from:
http://library.thinkquest.org/C0110248/algebra/islsurdlaw.htm