Surds and Indices Flashcards
What is an irational number?
An irrational number is a non - termiating, non - recurring decimal, hence it cannot be written as an integer over an integer.
E.g. root 2, root 7, pi
to write an irrational number between 2 numbers, write a rational and add non - terminating, non - recurring numbers, e.g 1.2401001000100001
Index Laws
a^0
a^1/m
a^n/m
a^-m
a^0 = 1
a^1/m = m root a
a^n/m = (m root a)^n
a^-m = 1/a^m
Surds Rules
root a x root a
root a x root b
root a / root b
root a x root a = a
root a x root b = root ab
root a / root b = root a/b
Index Laws
a^m x a^n
a^m / a^n
(a^m)^n
(a^m b^n)^x
a^n x b^n
a^m x a^n = a^m+n
a^m / a^n = a^m-n
(a^m)^n = a^mn
(a^m b^n)^x = a^mx b^nx
a^n x b^n = (ab)^n
When solving complex indices questions, what do you do?
make each componant equal to a few common base numbers then simplify