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**Q.1Â Â Â Â Â State whether the following statements are true or false. Justify your answers. Â Â Â Â Â Â Â Â Â Â Â (i) Every irrational number is a real number. Â Â Â Â Â Â Â Â Â Â Â (ii) Every point on the number line is of the form , where m is a natural number.Â Â Â Â Â Â Â Â Â Â Â (iii) Every real number is an irrational number.**

**(i)**Â Â Â Â Every irrational number is a real number - True** **

Â Â Â Â Â Â Â Â Justification : - A real number is either rational or irrational. **(ii)**Â Â Every point on the number line is of the form Â - False

Â Â Â Â Â Â Â Â Justification : - Numbers Â of other types also lie on the number line. **(iii)Â **Every real number is an irrational number - False

Â Â Â Â Â Â Â Â Â Justification : - Rational numbers are also real numbers.

**Q.2Â Â Â Â 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 numbers.**

**Sol. **

No, the square roots of all positive integers are not irrational.

Example : -Â 4 is a positive integer but is a Â natural number.

**Q.3Â Â Â Â Â Â Show how can be represented on the number line.**

**Sol.**

We shall now show how to represent on the number line.

We first represent on the number line l. We construct a right - angled OAB, right - angled at A such that OA = 2 and AB = 1 Â unit (see figure)

Then, Â

Now, we cut off a length on the number line.

Then the point C represents the irrational number .

**Q.4Â Â Â Â Â Classroom activity (Constructing the 'square root spiral') : Take a large sheet of paper and construct the 'square root spiral' in the following fashion.Â Start with a point O and draw a line segment of unit length. Draw a line segment perpendicular toÂ of unit Â length (see figure).Â Now draw a line segment perpendicular to . Then draw a line segment perpendicular to . Continuing in the manner, you can get the line segment by drawing a line segment of unit length perpendicular to . In this manner, you will have created the points and joined them to create a beautiful spiral depicting .**

* Sol.Â Â Â Â Â Â *Classroom activity - Do as directed.

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