Rational And Irrational Numbers | Class 9 ICSE Maths Selina Chapter 1 Exercise 1B Irrational numbers

Рет қаралды 9,109

LearnoHub - Class 9,10

Күн бұрын

Пікірлер: 16

@lalitasonar5848 Жыл бұрын

Thanku so much teacher I understood everything because of your teaching,I can finally give my test today

@M_A_G2010 5 ай бұрын

Irrational numbers have non-terminating, non-repeating decimal expansions. Proof of irrationality of numbers like √2, √5, and √5 - √3 is provided. Properties of irrational numbers, such as the sum, difference, product, and quotient, are discussed. Key moments: 00:41 Rational numbers are of the form a/b where a and b are integers, while irrational numbers have non-repeating, non-terminating decimal expansions like root 2. Pi is an example of an irrational number with a non-repeating decimal expansion. -Difference between rational and irrational numbers. Rational numbers are a/b with repeating or terminating decimals, while irrational numbers have non-repeating, non-terminating decimals like root 2. -Decimal expansion examples. Rational numbers like 0.6666 have repeating decimals, while irrational numbers like root 2 have non-repeating, non-terminating decimals. -Proof of root 2 being irrational. Assuming root 2 is rational leads to a contradiction, showing that root 2 cannot be expressed as a fraction of integers. 06:04 The video explains how to prove that square roots like root 2, root 5, and root 15 are irrational numbers using assumptions and mathematical steps. -Proving root 2 is irrational by showing it cannot be expressed as a rational number. Contradictory statements lead to the conclusion that root 2 is irrational. -Demonstrating the proof for root 5 being irrational by assuming it is rational, then showing that it leads to a contradiction, proving its irrationality. -Explaining the process of proving root 15 minus root 3 is irrational by assuming it is rational, performing mathematical operations, and reaching a contradiction. 12:13 Understanding the properties of rational and irrational numbers is crucial in mathematics. Contradictory statements arise when assuming a number is both rational and irrational, leading to the proof of irrationality in scenarios like root 5 minus root 3. -Contradictory statements occur when assuming a number is both rational and irrational, highlighting the importance of understanding number properties in mathematics. -The comparison of roots of rational numbers showcases how their relationships can determine the order of the numbers, providing insights into number comparisons. -Properties like the sum and product of rational and irrational numbers demonstrate how operations can result in either rational or irrational outcomes, contributing to a deeper understanding of number systems. 18:27 When adding two irrational numbers, the result can be rational or irrational. The sum of a rational and an irrational number is always irrational. -The difference of two irrational numbers can result in either a rational or an irrational number. -Multiplying an irrational number with a rational number results in a rational number. -The product of two rational numbers may or may not be rational, depending on the calculation. 24:22 When multiplying irrational numbers, the result can be rational or irrational. Dividing irrational numbers can result in either rational or irrational numbers. Inserting rational and irrational numbers between two values follows specific rules to obtain desired outcomes. -Multiplication and division of irrational numbers. It can yield rational or irrational results. -Inserting rational and irrational numbers between two values. Specific rules determine the outcome. 30:26 Understanding cube roots and rational numbers. Cube roots comparison and identification of rational and irrational numbers within real numbers. -Comparing cube roots and identifying the larger value. Explaining the concept with examples of cube roots of 3 and 4. -Explaining the concept of real numbers, including rational and irrational numbers. Defining the union of rational and irrational numbers as real numbers. -Differentiating rational and irrational numbers. Solving problems to determine if given numbers are rational or irrational based on their properties. 36:45 The video discusses rational and irrational numbers by analyzing expressions like root 3 plus root 2 to prove their nature. It also delves into sets of integers and non-negative integers, showcasing examples to illustrate the concepts. -Explanation of rational and irrational numbers through mathematical expressions like root 3 plus root 2. Proving irrationality by assuming rationality and squaring both sides for analysis. -Illustration of sets of integers, including negative numbers, positive numbers, and zero. Explanation of why fractions cannot be included in the set of integers. -Discussion on non-negative integers, where zero and positive integers are included in the set. Examples provided to clarify the concept of non-negative integers. 42:50 The video discusses the concept of rational and irrational numbers through examples and proofs. It demonstrates how to determine the order of numbers with roots and provides exercises on finding rational and irrational numbers. -Explanation of rational and irrational numbers through mathematical proofs and examples. -Determining the order of numbers with roots and comparing their magnitudes. -Exercise on finding rational and irrational numbers and placing them in ascending and descending order. 49:23 Understanding irrational numbers and their properties is crucial in mathematics. The video explains how to find irrational numbers between given roots and simplifies expressions involving roots. -Identifying irrational numbers between given roots and understanding why certain numbers are excluded due to being perfect squares. -Simplifying expressions involving roots by performing multiplication and division to obtain the final answer. -Exploring the properties of irrational numbers through addition, subtraction, multiplication, and division.