**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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