Indices, Surds & Logarithms
Indices and Surds, Logarithms Questions – Indices and Surds, Logarithms Quiz Details
Online Test Name | Indices and Surds, Logarithms |
Exam Type | Chapters & Multiple Choice Questions |
Category | Aptitude Quiz |
Number of Questions | 30 |
Important Formulas – Surds and Indices
Laws of Indices
an=a.a.a⋯(n times)
am.an…ap=am+n+…+p
am.an=am+n
aman=am−n
(am)n=amn=(an)m
(ab)n=anbn
(ab)n=anbn
a−n=1an
an=1a−n
a0=1 where a∈R,a≠0
ap/q=apq
if am=an where a≠0 and a≠±1, then m=n
if an=bn where n≠0, then a=±b
Surds
Let a be a rational number and n be a positive integer such that an is irrational. Then an is called a surd of order n.
Examples:
- 3 is a surd of order 2
- 73 is a surd of order 3
- 43 is a surd of order 2
Please note that numbers like 9, 273 etc are not surds because they are not irrational numbers.
Every surd is an irrational number. But every irrational number is not a surd. (eg : π , e etc are not surds though they are irrational numbers.)
Quadratic Surds
A surd of order 2 is called a quadratic surd
Examples
2,3,(3+5), etc.
Rules of Surds
mn=mn
a.a.a⋯n times=a1−12n
a.a.a⋯∞=a
if a+a+a⋯∞=p, then p(p−1)=a
The conjugate surd of a+b=±(a−b)
if b and d are quadratic surds and if a+b=c+d,
then a=c and b=d
That is, rational part on left side = rational part on right side.
and irrational part on left side = irrational part on right side.
if b and d are quadratic surds and if a+b=d,
then a=0 and
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