Surds and Indices Flashcards

1
Q

What is an irational number?

A

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

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2
Q

Index Laws
a^0
a^1/m
a^n/m
a^-m

A

a^0 = 1
a^1/m = m root a
a^n/m = (m root a)^n
a^-m = 1/a^m

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3
Q

Surds Rules
root a x root a
root a x root b
root a / root b

A

root a x root a = a
root a x root b = root ab
root a / root b = root a/b

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4
Q

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

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

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5
Q

When solving complex indices questions, what do you do?

A

make each componant equal to a few common base numbers then simplify

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6
Q
A
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