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Chapter 2: System of Real Numbers, Exponents and Radicals (70 videos)

2.1: Properties of Rational Numbers
1. Introduction to Rational Numbers
2. Problem 1: Introduction to Rational Numbers
 
2.2: Decimal Fractions as Rational and Irrational Numbers
1. Decimal Representation of Rational Number
2. Problem 1: Decimal Representation of Rational Number
3. Decimal Representation of Irrational Number
 
2.3: Set of Real Numbers
1. Introduction to Real Numbers
 
2.4: Properties of Real Numbers
1. Closure Law of Rational Numbers
2. Problem 1: Closure Law of Rational Numbers
3. Commutative Law
4. Associative Law
5. Problem 1: Associative Law
6. Additive Identity & Additive Inverse
7. Problem 1: Additive Identity & Additive Inverse
8. Multiplicative Identity & Inverse
9. Problem 1: Multiplicative Identity & Inverse
10. Distributive Law
11. Problem 1: Distributive Law
12. Trichotomy Property of Inequality
13. Problem 1: Trichotomy Property of Inequality
 
2.5: Properties of Equality of Real Numbers
1. Reflexive And Symmetric Property of Equality
2. Transitive Property of Equality
3. Problem 1: Transitive Property of Equality
4. Additive Property of Equality
5. Multiplicative Property of Equality
6. Cancellation Property of Equality
7. Problem 1: Cancellation Property of Equality
 
2.6: Properties of Inequality of Real Numbers
1. Archimedian Property of Inequality
2. Transitive Property of Inequality
3. Problem 1: Transitive Property of Inequality
4. Additive Property of Inequality
5. Multiplicative Property of Inequality
6. Problem 1: Multiplicative Property of Inequality
 
2.7: Exponent
1. Exponent or Index Definition
2. Problem 1: Exponent or Index Definition
 
2.8: Laws of Exponents
1. Law of Sum of Power of Exponents
2. Problem 1: Law of Sum of Power of Exponents
3. Law of Power of Product of Exponent
4. Problem 1: Law of Power of Product of Exponent
5. Law of Power of Power of Exponent
6. Problem 1: Law of Power of Power of Exponent
7. Law of Quotient of Power with Same Base
8. Problem 1: Law of Quotient of Power with Same Base
9. Law of Power of a Fraction
10. Problem 1: Law of Power of a Fraction
 
2.9: Radicals and Square Root of Positive Real Number
1. Introduction to Radical
2. Square Root
3. Problem 1: Square Root
4. Properties of Square Root
5. Problem 1: Properties of Square Root
6. More on Properties of Square Root
 
2.10: The nth Root of a Positive Real Number
1. qth Root of x
2. Problem 1: qth Root of x
3. Properties of qth Root of x
4. Problem 1: Properties of qth Root of x
 
2.11: Rational Exponents
1. Rational Exponents
2. Problem 1: Rational Exponents
3. Properties of Rational Exponents
4. Problem 1: Properties of Rational Exponents
 
2.12: Surds
1. Introduction to Surds
2. Problem 1: Introduction to Surds
3. Addition & Subtraction of Surds
4. Problem 1: Addition & Subtraction of Surds
5. Problem 2: Addition & Subtraction of Surds
6. Multiplication & Division of Surds
7. Problem 1: Multiplication & Division of Surds
8. Problem 2: Multiplication & Division of Surds
9. Introduction to Rationalization
10. Rationalizing Denominator & its Types
11. Problem 1: Rationalizing Denominator & its Types
12. Problem 2: Rationalizing Denominator & its Types
 

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