Lesson Summary 14/2/13 Ryan Tan

Surds

Important = *

*

(2√3)^2

=2√3 x 2√3

=4√3√3

=4(√3)^2

=4(3)

=12

Conjugate Surds

*

(a+b)(a-b) = a^2 - b^2

(√a+√b)(√a-√b)=(√a)^2-(√b)^2

(a^1/2 + b^1/2) (a^1/2 - b^1/2) = (a^1/2)^2 - (b^1/2)^2

2√3^2=

a) 2√3 √3 (correct)

b)2(√3)^2 (correct)

c)2 . 3^1/2x2 (correct)

d) 4(3) (wrong)

e) √4(3) ^2 (wrong)

f) √4 √9 (wrong)

To convert irrational surds into rational surds

By similar surd

1/√2 x √2(to both numerator and denominator)

= √2 /2

By conjugate surd

(1/ √3 - √2) x √3 + √2 (to both numerator and denominator)

=√3 + √2/ 3-2

=√3 + √2 / 1