Best explanation to understand and solve the surds and indices problems.

In this section, you will have aptitude questions based on surds and indices.

This is one of the important and a complicated section in any aptitude exams. But we will make it easy for you.

Learn about what is surds and indices, important formulas and tricks to solve the aptitude questions easily through our website and get a high score in your exams.

What Is Surd?

Surds are numbers which cannot be simplified or whose square roots or cube roots cannot be removed. In other words , we cannot find the exact value of surds.

For Example: What is the answer for 4 (square root of 4). The answer is very simple. It is 2.

But what is the answer for 2. There is no exact answer for this. This because we cannot remove the square root. So this is called a surd.

Types Of Surds

The following are the various types of surds:- 

 Simple Surds: Surds which consists of only one term is called simple surd.

 For example,5,7, 55, 2, etc. 

Similar Surds – If the surds having the same common surds factor, or in other words, they are different multiples of the same surd, then they are called similar surds.

Pure Surds – Surds which are wholly irrational are called pure surds.

Mixed Surds – Surds which are not wholly irrational and can be expressed as a product of a rational number and an irrational number is called mixed surd.

Binomial Surds – A surd which is made up of two other surds is called binomial surd.

Compound Surds – An expression which is the addition or subtraction of two or more surds is called compound surd.

Important Rules Of Surds

RULE 1: a x b = ax b

RULE 2: a/b=  a /b

What Is Index Or Indices?

An index or indices (plural form of index) is an exponent or power of a number . 

For Example : a3 In this, 3 is the power or exponent of a. So 3 is the index of a.

Important Laws Of Indices

There are three important laws in indices. They are as follows

Law 1: anx am= a(n+m)

The first laws is that when two identical numbers with different exponents are to be multiplied, then add the two exponent. The answer will be the same if we multiply the number without adding the powers. But this law makes the calculation easier.

For Example: 22x 23= 2(2+3)

Therefore the answer will be 25which is equal to 32.

Law 2: am / an  = a(m-n)

This law says that if two identical numbers are divided with different exponents, then the two exponents are to be subtracted. 

For Example: 44/ 42 = 4(4-2)

 Therefore the answer will be 42 which is equal to 16.

Law 3: (am) n = a(m x n)

The last law says that we have to multiply a power in the bracket with power outside the bracket if there are two power for the same number.

For Example: (22)2=  2(2 X 2)

Therefore the answer will be 24 which is equal to 32.

These are the very important rules of indices.

Law Of ‘to The Power Of Zero’ In Indices

a0 = 1

One more  important law of indices which is derived from the second law is that anything to the power of ‘0’ is equal to ‘1’. 

For Example: a2 / a2 = a (2-2)

Therefore the equation will become a0 which is equal to 1