Chapter 1 · Class 9 ICSE · Formula Sheet

Rational & Irrational Numbers Formulas — Class 9 ICSE

Distinguish between rational and irrational numbers and represent them on the number line.

Key Formulas

Rationalizing

\dfrac{1}{\sqrt{a}} = \dfrac{\sqrt{a}}{a}

Rationalizing Binomial

\dfrac{1}{a + \sqrt{b}} = \dfrac{a - \sqrt{b}}{a^2 - b}

Surds Property

\sqrt{a} \times \sqrt{b} = \sqrt{ab}

Division of Surds

\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}

Worked Examples

1Using: Place Value

Find the place value of 6 in 3,65,421.

Step 1: 6 is in the ten-thousands place.

Step 2: Place value = 6 x 10,000 = 60,000.

Answer: 60,000

2Using: Successor

Find the successor of 9,999.

Step 1: Successor = n + 1

Step 2: = 9,999 + 1 = 10,000.

Answer: 10,000

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Frequently Asked Questions

How many formulas are in Class 9 ICSE Rational & Irrational Numbers?+
There are 4 formulas in the Rational & Irrational Numbers chapter for Class 9 ICSE. Each formula is essential for solving problems in this topic.
How to remember Rational & Irrational Numbers formulas easily?+
Practice regularly with worked examples, group related formulas together, and use SparkEd's interactive practice mode to reinforce your memory through problem-solving.
Are these Rational & Irrational Numbers formulas enough for exams?+
Yes, these formulas cover the complete ICSE Class 9 syllabus for Rational & Irrational Numbers. Practice applying them to different types of questions for full exam readiness.

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