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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!**

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.

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**Introduction to Surds and Indices:
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.

**– A Rational Number is a real 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.**

*Rational Number***– An irrational Number is a number that cannot be expressed as a/b, and when expressed as a decimal it cannot be expressed using a finite number of digits.**

*Irrational Number***– An irrational n**

*Surd*^{th }root 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.

**– The power to which a number is 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.**

*Index*
Indices are
useful in expressing large numbers in a simpler form.

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**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.

**Law 1**

When bases
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.

**Law 3**

When the
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.

**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.

**Law 6**

Any number
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.

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

Let’s look
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

**Law 2**

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

**Law 3**

We reach
this expression using the 1

^{st}Law of Surds and the Law of Indices.**Law 4**

We reach
this expression using the 1

^{st}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 1

^{st}Law of Surds and the Law of Indices.
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