Page 10 - Math SL HB Sem 1

INDICES.I-OCARII'] I MS.SURDS

3. SIIRI)S

Any number in the form db , rvhich cannot be rvritten as a liaction of two integers is

called surd with n is the index and b the radicand.
Properties of Surds:

@) dv =*

(b) dt ={; {,
t; ,V;
(c)
lIv {,

Notes: ( | ) T- +y r .t7 *,[l
1

(2) x7 +2xy+ y? = (x + 1,)2 -;s1,

-
Conjugates ofsurds: t Ji + Ji I and ( Ja ..6 are conjugate ofeach otlrer.
)
di*Ji)d; Ji)=a- u
Rationalizing the denominators:
- eliminatc thc surds lrorn thc denonrinator by multiply thc numcrator and

denominator by a suitablc tactor, this rvill lcave thi. denominator lree ol'
surds.
33GJ 3Jx I
Example: (a)
r/;r- I r/x I J.;r-l -rl

t l^ t ,,8
tri lZA 'J3b' \lza' b'^13'b
- r_-
- t---- -
1l 3r' - w ,*t, .*t, ;t-;
(b) '.13b'
2.32a2b '.lts t b

'a,f:ir' 3b

t-2