Powers, Indices and Surds Notes For CTET Exam: Free PDF

Mathematics is an equally important section for CTET, MPTET, HTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts, Facts and Formulae of the Powers, Indices and Surds.

To let you make the most of Mathematics section, we are providing important facts related to the Powers, Indices and Surds. At least 2-3 questions are asked from these topics in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

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Powers, Indices and Surds

Type – I


⟹ Let n be a positive integer and a be real number, then:

is called “n­­­­­­­­­­­­th Power of a” or

“a raised to the power n”

where, a is called the base and n is called index or exponent of the power .

E.x. 3² = square of 3, 3³ = cube of 3 etc.

Laws of Indices:

Mathematics Study Notes For All Teaching Exams

These rules are also true when n is negative or fraction.

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Type – II

Important Formula Based on Surds:


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Similar or like Surds: Surds having same irrational factors are called “similar or like surd”.

Unlike surds: Surds have non – common irrational factors are called “unlike surds”.

Type III

 Comparison of Surds: (i) If two surds are of the same order, then the one whose radicand is larger, is the larger of the two.

(ii) If two surds are distinct order, we change them into the surds of the same order.

This order is L.C. M. of the orders of the given surds.

CTET Maths complete Study Notes 

Type – IV

Type – V

Square – root of an irrational number:

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