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Formula Sheet

Real Numbers — Formula Sheet

Tamil Nadu Board · Class 9 · Mathematics

8 formulas from Real Numbers (Tamil Nadu Board Class 9 Mathematics) on one page, grouped by topic. Includes Non-Terminating Recurring, Irrational numbers.

45 questions25 flashcards8 formulas & key relations5 concepts

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A nested Venn diagram illustrating the relationships between natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) as subsets of each other.
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8 Entries · 4 Sections

Formulas and Key Relations

Decimal Representation and Denseness Property

Non-Terminating Recurring Decimal

Decimal repeats a block of digits indefinitely (e.g., 1/3 = 0.333..., 2/7 = 0.285714285714...)

Irrational Numbers and Surds

Irrational numbers

√2, √3, √5, π, e, φ (golden ratio), etc.

√n is irrational if n is not a perfect square

If a is rational and √b is irrational, then a+√b, a-√b, a√b, a/√b are all irrational

Operations on Surds: Simplification and Manipulation

Law 1

(ⁿ√a)ⁿ = a = ⁿ√(aⁿ) - Taking root and raising to power are inverse operations

Law 2

ⁿ√a × ⁿ√b = ⁿ√(ab) - Product of roots = root of product (same index only)

Law 3

ⁿ√(ᵐ√a) = ⁿᵐ√a = ᵐ√(ⁿ√a) - Roots can be combined multiplicatively

Key relations

Examples

1/2, 3/4, -5/7, 0.5 = 1/2.

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Frequently Asked Questions

What are the important topics in Real Numbers for Tamil Nadu Board Class 9 Mathematics?
Key topics in Real Numbers include Classification of Numbers: From Natural Numbers to Real Numbers, Decimal Representation and Denseness Property, Irrational Numbers and Surds, Operations on Surds: Simplification and Manipulation. Study these first, then practise questions on each for Class 9 exams.
How many formulas are in Real Numbers?
This sheet lists 8 formulas from Real Numbers, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
How should I revise Real Numbers for Class 9 exams?
Learn the core ideas first, then work through the 45 practice questions on Real Numbers. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Real Numbers

All Tamil Nadu Board Class 9 Mathematics Formula Sheet

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