Real Numbers
Mathematics Solutions from Chapter -1 - Real Numbers
This chapter covers topics, such as Euclid's Division Lemma, The Fundamental Theorem of Arithmetic, Irrational Numbers, HCF and LCM & Rational Numbers and Their Decimal Expansions etc.
Practice Other Topics from Real Numbers
This topic covers concepts, such as Natural Numbers, Real Numbers, LCM and HCF of Numbers, Least Common Multiple (LCM), Highest Common Factor (HCF), Lemma, Algorithm, Euclid’s Division Lemma, Euclid Division Algorithm, HCF of Two Positive Integers using Euclid’s Division Algorithm, Positive Even Integers of the Form (2q), Positive Odd Integers of the Form (2q+1), Positive Odd Integers of the Form (4q+1, 4q+3), Positive Even Integers of the Form (4q, 4q+2), General Form of Square of a Positive Integer (3m, 3m+1), General Form of Cube of a Positive Integer (9m, 9m+1 & or 9m+8) etc.
This topic covers concepts, such as Fundamental Theorem of Arithmetic, Factorisation of a Positive Integer & Composite Numbers as Product of Primes etc.
This topic covers concepts, such as HCF using Prime Factorisation Method, LCM using Prime Factorisation Method, Relation between LCM and HCF of Two Numbers, HCF of Three Positive Integers & LCM of Three Positive Integers etc.
This topic covers concepts, such as Irrational Numbers, Properties of Irrational Numbers, Sum of Rational and Irrational Numbers, Difference of Rational and Irrational Numbers, Multiplication of Rational and Irrational Numbers, Division of Rational and Irrational Numbers, Sum of Two Irrational Numbers, Difference of Two Irrational Numbers, Multiplication of Two Irrational Numbers, Division of Two Irrational Numbers, Establishing Irrationality of Numbers of Form √a, b- √a and b√a, Establishing Irrationality of Numbers of Form √a, a is Not Perfect Square, Establishing Irrationality of Square Roots of Two / Three, Establishing Irrationality of Numbers of Form b - √a & Establishing Irrationality of Numbers of Form b√a etc.
This topic covers concepts, such as Rational Numbers, Prime Factorisation of Denominators of Rational Numbers, Prime Factorisation of Denominators of Rational Numbers Having Terminating Decimal & Prime Factorisation of Denominators of Rational Numbers Having Non-terminating Decimal etc.
