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That is, \(\pi = \frac{c}{d} \) . This seems to contradict the fact that \(\pi\) is irrational.

How will you resolve this contradiction?

Answer :

First of all, there is not any contradiction. \(\pi\) defined here has an approximate value of \(\frac{22}{7} \) i.e. by comparing with \(\frac{c}{d} \) .

Also, any value measured on scale or physically is an approx value.

- Classify the following numbers as rational or irrational :i)\(2 - \sqrt{5}\)ii)\((3 + \sqrt{23}) - \sqrt{23}\)iii)\( \frac{2\sqrt{7} }{ 7\sqrt{7}} \)iv)\(\frac{1}{\sqrt{2}} \)v)\(2\pi\)
- Simplify each of the following expressions: i) \((3 + \sqrt{3})(2 + \sqrt{2})\)ii) \((3 + \sqrt{3})(3 - \sqrt{3})\)iii) \( (\sqrt{5} + \sqrt{2})(\sqrt{5} + \sqrt{2})\)iv)\((\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})\)
- Represent \(\sqrt{9.3}\) on the number line.
- Rationalize the denominator of the following : i)\(\frac{1}{\sqrt{7}} \)ii)\( \frac{1}{\sqrt{7} } - \sqrt{6} \)iii)\(\frac{1}{\sqrt{5}} + \sqrt{2} \)iv)\(\frac{1}{\sqrt{7}} - 2 \)

- NCERT solutions for class 9 maths chapter 1 Number Systems
- NCERT solutions for class 9 maths chapter 2 Polynomials
- NCERT solutions for class 9 maths chapter 3 Coordinate geometry
- NCERT solutions for class 9 maths chapter 4 Linear equations in two variables
- NCERT solutions for class 9 maths chapter 5 Introduction to Euclidean Geometry
- NCERT solutions for class 9 maths chapter 6 Lines and Angles
- NCERT solutions for class 9 maths chapter 7 Triangles
- NCERT solutions for class 9 maths chapter 8 Quadrilaterals
- NCERT solutions for class 9 maths chapter 9 Areas of parallelograms and triangles
- NCERT solutions for class 9 maths chapter 10 Circles
- NCERT solutions for class 9 maths chapter 11 Constructions
- NCERT solutions for class 9 maths chapter 12 Heron's Formula
- NCERT solutions for class 9 maths chapter 13 Surface areas and volumes
- NCERT solutions for class 9 maths chapter 14 Statistics
- NCERT solutions for class 9 maths chapter 15 Probability

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- NCERT solutions for class 9 science chapter 2 Is Matter Around Us Pure
- NCERT solutions for class 9 science chapter 3 Atoms and Molecules
- NCERT solutions for class 9 science chapter 4 Structure of the Atom
- NCERT solutions for class 9 science chapter 5 The Fundamental Unit of Life
- NCERT solutions for class 9 science chapter 6 Tissues and Fundamental unit of life
- NCERT solutions for class 9 science chapter 7 Diversity in Living Organisms
- NCERT solutions for class 9 science chapter 8 Motion
- NCERT solutions for class 9 science chapter 9 Force and Laws of Motion
- NCERT solutions for class 9 science chapter 10 Gravitation
- NCERT solutions for class 9 science chapter 11 Work and Energy
- NCERT solutions for class 9 science chapter 12 sound
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- NCERT solutions for class 9 science chapter 15 Improvement in Food Resources