Friday, 9 June 2017

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!

surds and indices
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.
surds and indices
surds and indices
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.
surds and indices
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’.
surds and indices
surds and indices
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.
surds and indices
Indices are useful in expressing large numbers in a simpler form.
surds and indices

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
surds and indices
When bases are equal and the numbers are being multiplied, then we add the powers.
Law 2
surds and indices
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
surds and indices
When the same base is raised to power twice, then the two indices are multiplied.
Law 4
surds and indices
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
surds and indices
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
surds and indices
Any number raised to the power 0 is equal to 1.
Law 7
surds and indices
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
surds and indices
Nth root of a number can be expressed as the number raised to the power 1/n
Law 2
surds and indices
The common radical power can be split when two numbers are multiplied or divided

Law 3
surds and indices
We reach this expression using the 1st Law of Surds and the Law of Indices.
Law 4
surds and indices
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
surds and indices
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.
surds and indices
surds and indices
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