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Answer :

Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion.

Start with a point O and draw a line segment \(OP_1\) of unit length. Draw a line segment \(P_1P_2\) perpendicular to \(OP_1\) of unit length.

Now, draw a line segment \(P_2P_3\) perpendicular to \(OP_2\) . Then draw a line segment \(P_3P_4\) perpendicular to \(OP_3\).

Continuing in this manner, you can get the line segment \(P_(n-1)Pn\) by drawing a line segment of unit length perpendicular to \(OP_(n-1)\) .

In This manner, you will have created the points \(P_2\), \(P_3\), \(P_4\), \(P_5\),........ and joined them to create a beautiful spiral depicting \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{4}\),......

- State whether the following statements are true or false. Justify your answers.i) Every irrational number is a real number.ii) Every point on the number line is of the form \(\sqrt{m}\) , where m is a natural number.iii)Every real number is an irrational number.
- Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
- Show how \(\sqrt{5}\) can be represented on the number line.

- 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
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- 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
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