Page 10 - Math SL HB Sem 1

INDICES.I-OGARIf I]MS.SI.]Rt)S

J. SUITDS
Any number in the form db , rvhich cannot be written as a fraction of two integers is

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

(a) i/7=r

(b) d, ={; {,

n d;
(c)
il, 6

f , f ,
Notes: (t) jI- +y2 * r/-t' + 1.1'-

(2) x'+2xy+y'- (x+ 1')2 = x1y

Conjugates ofsurds: < Ji*Jil and ( Ja .,6 are conjugate ofeach other.
)
tJitJildi-Jtl=a- o

Rational izing the denominators:
- eliminate the surds lrom the denominator by multiply the numerator and
denominator by a suitable factor, tlris will leave the denominator free ol'

surds.
3 ,.EJ
3 3.,tSi
Example: (a) :x:
Ji:=r Jx I Jx-l .rl

"Ei - 'Jr.' 'J;; '$b' 'Jrn x b.$, b
:x:
\i 3b' 4;; 'Jlt' 'Jlt' 'Jlb' il:t+
(b)
2-3'a'b Vt8"%
\fi%' 3b

t-2