Real Numbers — Formula Sheet
Karnataka Board · Class 10 · Mathematics
5 formulas from Real Numbers (Karnataka Board Class 10 Mathematics) on one page, grouped by topic. Includes Example, Example and For any two positive.
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Formulas and Key Relations
Revisiting Irrational Numbers
√2, √3, √5, and √p (where p is prime) are all irrational
Key relations
Example
For 72 = 2³ × 3² and 48 = 2⁴ × 3, HCF = 2³ × 3¹ = 24.
Example
For 72 = 2³ × 3² and 48 = 2⁴ × 3, LCM = 2⁴ × 3² = 144.
For any two positive integers a and b
HCF(a,b) × LCM(a,b) = a × b.
Example
For 72 and 48, HCF = 24, LCM = 144, and 24 × 144 = 72 × 48 = 3456.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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