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Exercise - 1.2

Number Systems

**Question-1 :-** 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 √m, where m is a natural number.
(iii) Every real number is an irrational number.

(i) True; since the collection of real numbers is made up of rational and irrational numbers. (ii) False; as negative numbers cannot be expressed as the square root of any other no. e.g. √-4, √-9 etc. (iii) False; as real numbers include both rational and irrational numbers. Therefore, every real no. cannot be an irrational no.

**Question-2 :-** 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.

If numbers such as √36=6 and √49=7 are considered, Then here, 6 and 7 are rational numbers. Thus, the square roots of all positive integers are not irrational.

**Question-3 :-** Show how √5 can be represented on the number line.

```
Using Pythagoras theorem that OB=√ 1²+4² =√5
By using the compass, with centre O and radius OB, draw an arc which intersecting the number line at the point P.
Then P corresponds to √5 on the number line.
```

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