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Real Number Class 10 | Maths Chapter 1 | Full Chapter | Number System | Rational Numbers | CBSE

Dear Sir・34 minutes read

The Dear Sir's court trial focuses on 10th class chapters regarding Real Numbers, explaining the distinction between real, integers, positives, negatives, rational, and irrational numbers. Prime and composite numbers, LCM, HCF, and coprime numbers are discussed, along with practical applications and examples, highlighting the importance and relationships between these concepts.

Insights

  • Real Numbers serve as the foundation for all other number types, including integers, positives, negatives, rational, and irrational numbers, highlighting their fundamental role in mathematics.
  • The concept of coprime numbers, exemplified by pairs like three and four or five and six, showcases numbers that share only one common factor, emphasizing the significance of this relationship beyond prime numbers and its application in determining irrationality, as seen in the case of the square root of three.

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Recent questions

  • What is the Fundamental Theorem of Arithmetic?

    The Fundamental Theorem of Arithmetic states that any composite number can be expressed as a product of prime numbers.

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Summary

00:00

"Exploring Real Numbers in 10th Class"

  • The trial of the country is commencing in Dear Sir's court, focusing on the 10th class chapters.
  • Children in the new 10th class are encouraged to like and subscribe to the Dear Sir channel.
  • The first chapter discussed is Real Numbers, emphasizing the distinction between real and other numbers.
  • Real Numbers explain that all numbers originate from them, including integers, positives, negatives, rational, and irrational numbers.
  • The Fundamental Theorem of Arithmetic in class 10th involves prime and composite numbers.
  • Prime numbers are those divisible only by themselves or one, while composite numbers have more than two factors.
  • The theorem states that any composite number can be written as a multiplication of prime numbers.
  • To prove a root number irrational, assume it's rational and then disprove it, showing it's irrational.
  • The process involves accepting the number as rational and then proving it wrong to establish its irrationality.
  • Prime factorization involves breaking down numbers into prime factors through division by the smallest possible prime numbers.

12:48

Calculating LCM and HCF Relationship in Numbers

  • Given two numbers, find their LCM and HCF.
  • Verify the relationship that the product of LCM and HCF equals the product of the two numbers.
  • Example: Calculate LCM and HCF for the numbers 510 and 92.
  • Factors of 510: 2, 3, 5, 17. Factors of 92: 2, 2, 23.
  • LCM is calculated by multiplying all numbers except the HCF.
  • HCF of 510 and 92 is 2.
  • LCM of 510 and 92 is 23460.
  • Verify the relationship by multiplying LCM and HCF, and the two numbers.
  • Relationship confirmed: LCM * HCF = Number1 * Number2.
  • Understanding the practical application of LCM and HCF in various scenarios.

24:37

Understanding Coprime Numbers with Examples

  • Coprime numbers are those with only one common factor, which is one.
  • Illustration using the numbers three and four to explain coprime numbers.
  • Coprime numbers do not share any factors except one.
  • The concept of coprime numbers applies to any type of number, not just primes.
  • Example with the numbers five and six to demonstrate coprime numbers.
  • If two numbers share any factor other than one, they are not coprime.
  • The proof that the square root of three is an irrational number based on the concept of coprime numbers.
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