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.
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:
These rules are also true when n is negative or fraction.
Type – II
Important Formula Based on Surds:
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”.
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.
Type – IV
Type – V
Square – root of an irrational number: