# Surds and Indices I- Important Terms and Laws in Indices and Surds for SSC Exams

### 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.

### 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.

Rational Number – 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.
Irrational 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.
Surd – An irrational nth 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.

Index – 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.
Indices are 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.
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 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.
Law 5
We reach this expression using the 1st Law of Surds and the Law of Indices.

Using these laws we can solve questions on surds and indices.
Stay tuned for more on this topic and keep preparing for Bank and SSC Exams.