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**Q.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 âˆšm , where m is a natural number.(iii) Every real number is an irrational number.Ans.**

Ans.

REMEMBER

According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In the figure: OB^{2}=OA^{2}+ AB^{2}

If OB^{2}=12 + 12 = 2 â‡’ OB = âˆš2

**Q.3. Show how âˆš5 can be represented on the number line.Ans.** Let us take the horizontal line XOX" as the x-axis. Mark O as its origin such that it represents 0.

Cut off OA = 1 unit, AB = 1 unit.

âˆ´ OB = 2 units Draw a perpendicular BC âŠ¥ OX.

Cut off BC = 1 unit.

Since OBC is a right triangle.

âˆ´ OB2 + OC^{2} = OC^{2}

or 2^{2} + 1^{2} = OC^{2} or 4 + 1 = OC^{2}

or OC^{2} = 5

â‡’ OC = âˆš5

With O as centre and OC as radius, draw an arc intersecting OX at D.

Since

âˆ´ OD represents âˆš5 on XOX".

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