Show that 3 + √5 is irrational.
CBSE Class 10 Real Numbers — Complete Guide
Real Numbers is the foundation chapter of CBSE Class 10 Mathematics, carrying approximately 6 marks in the board exam. This chapter covers Euclid's division algorithm, the Fundamental Theorem of Arithmetic, irrational number proofs, and decimal expansions of rational numbers.
Quick Revision: Key Concepts
- Euclid's Division Lemma: a = bq + r (0 ≤ r < b) — used to find HCF
- Fundamental Theorem: Every composite number = unique product of primes
- HCF: Common primes with smallest powers | LCM: All primes with greatest powers
- HCF × LCM = Product of two numbers
- Irrationality: √2, √3, √5 are irrational (proof by contradiction)
- Terminating decimals: p/q terminates iff q = 2m × 5n
Board Exam Pattern
Typically 2-3 MCQs (1 mark each) on HCF/LCM and decimal expansions, plus 1 short answer question (2-3 marks) on irrationality proof or Euclid's algorithm. Total: approximately 6 marks.
Most Important Questions
- Find HCF using Euclid's algorithm
- Find HCF and LCM using prime factorisation and verify HCF × LCM = product
- Prove √2 (or √3 or √5) is irrational
- Determine if decimal expansion is terminating or non-terminating
About Bright Tutorials
Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.