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**Questions on surds and indices appear**

to be very challenging and time taking, especially when they come in exams like

SSC CGL. This blog has all the important concepts and laws that will you solve

questions on surds and indices in a few seconds!

to be very challenging and time taking, especially when they come in exams like

SSC CGL. This blog has all the important concepts and laws that will you solve

questions on surds and indices in a few seconds!

SSC CGL exam

is one of the few competitive exams that has surds and indices on the syllabus.

Every year there are a couple if not more, questions on surds and indices in

the SSC CGL Exam and the SSC CGL 2017 Exam is expected to be no different. This

makes it an extremely important topic for you to not only understand but also

master. In the two blog series on surds and indices, we will start with

discussing the important terms, laws and concepts and then move to questions on

surds and indices in the second blog.

is one of the few competitive exams that has surds and indices on the syllabus.

Every year there are a couple if not more, questions on surds and indices in

the SSC CGL Exam and the SSC CGL 2017 Exam is expected to be no different. This

makes it an extremely important topic for you to not only understand but also

master. In the two blog series on surds and indices, we will start with

discussing the important terms, laws and concepts and then move to questions on

surds and indices in the second blog.

###
**Introduction to Surds and Indices:**

Important Terms

Important Terms

Before we

move ahead to the list of important laws that are used in solving questions on

surds and indices, we need to discuss some important terms that constitutes

these laws in surd and indices.

move ahead to the list of important laws that are used in solving questions on

surds and indices, we need to discuss some important terms that constitutes

these laws in surd and indices.

**– A Rational Number is a real number**

*Rational Number*that can be expressed as a simple fraction, i.e. it can be expressed as a

ratio. It can be expressed as a/b, where a and b are integers and b is not

equal to zero.

**– An irrational Number is a number that cannot be**

*Irrational Number*expressed as a/b, and when expressed as a decimal it cannot be expressed using

a finite number of digits.

**– An irrational nth root**

*Surd*of a positive integer is called a surd. In the expression below ‘a’ is the ‘radicand’,

the ‘root symbol’ is called the ‘radical sign’ and ‘n’ is known as the ‘radical

power’.

Remember

that- Every surd is a root but every root is not a surd. The decimal value of

such a fraction is always not terminating.

that- Every surd is a root but every root is not a surd. The decimal value of

such a fraction is always not terminating.

**– The power to which a number is**

*Index*raised is called the index. When a particular number ‘a’ is multiplied by

itself ‘n’ number of times, it is called index. Here ‘a’ is the ‘base’ and ‘n’

is the index.

Indices are

useful in expressing large numbers in a simpler form.

useful in expressing large numbers in a simpler form.

###
**Surds and Indices: Laws of Indices**

Before we

start discussing solution of problems from surds and indices, we need to

discuss the list of important laws tat are used in solving questions on surds

and indices.

start discussing solution of problems from surds and indices, we need to

discuss the list of important laws tat are used in solving questions on surds

and indices.

**Law 1**

When bases

are equal and the numbers are being multiplied, then we add the powers.

are equal and the numbers are being multiplied, then we add the powers.

**Law 2**

When bases

are equal and the numbers are being divided, then we subtract the power of the

denominator from the power of the numerator.

are equal and the numbers are being divided, then we subtract the power of the

denominator from the power of the numerator.

**Law 3**

When the

same base is raised to power twice, then the two indices are multiplied.

same base is raised to power twice, then the two indices are multiplied.

**Law 4**

When the bases

are different but the powers are equal and the numbers are multiplied, in such

cases the bases can be directly multiplied.

are different but the powers are equal and the numbers are multiplied, in such

cases the bases can be directly multiplied.

**Law 5**

When the

bases are different but the powers are equal and the numbers are divided, in

such cases the bases can be directly divided.

bases are different but the powers are equal and the numbers are divided, in

such cases the bases can be directly divided.

**Law 6**

Any number

raised to the power 0 is equal to 1.

raised to the power 0 is equal to 1.

**Law 7**

When a power

is in the denominator, on being taken in the numerator it becomes negative.

is in the denominator, on being taken in the numerator it becomes negative.

###
**Surds and Indices: Laws of Surds**

Let’s look

at laws of surds, which are used extensively in solving questions on surds and

indices.

at laws of surds, which are used extensively in solving questions on surds and

indices.

**Law 1**

Nth root of

a number can be expressed as the number raised to the power 1/n

a number can be expressed as the number raised to the power 1/n

**Law 2**

The common

radical power can be split when two numbers are multiplied or divided

radical power can be split when two numbers are multiplied or divided

**Law 3**

We reach

this expression using the 1st Law of Surds and the Law of Indices.

this expression using the 1st Law of Surds and the Law of Indices.

**Law 4**

We reach

this expression using the 1st Law of Surds and the Law of Indices,

unlike the previous law, the powers here are same.

this expression using the 1st Law of Surds and the Law of Indices,

unlike the previous law, the powers here are same.

**Law 5**

We reach

this expression using the 1st Law of Surds and the Law of Indices.

this expression using the 1st Law of Surds and the Law of Indices.

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