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Represent the following irrational numbers on the number line.

(i) \(\sqrt{3}\)

(ii) \(\sqrt{4.7}\)

(iii) \(\sqrt{6.5}\)

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(i) \(\sqrt{3}\)

(i) Draw a line and mark a point A on it. 

(ii) Mark a point B such that AB = 3 cm. 

(iii) Mark a point C on this line such that BC = 1 unit.

(ii) \(\sqrt{4.7}\)

(i) Draw a line and mark a point A on it. 

(ii) Mark a point B such that AB = 4.7 cm. 

(iii) Mark a point C on this line such that BC = 1 unit.

(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O. 

(v) With O as center and OC = OA as radius, draw a semicircle. 

(vi) Draw a line BD, which is perpendicular to AB at B. 

(vii) Now BD = \(\sqrt{4.7}\), which can be marked in the number line as the value of BE = BD = \(\sqrt{4.7}\)

(iii) \(\sqrt{6.5}\)

(i) Draw a line and mark a point A on it. 

(ii) Mark a point B such that AB = 6.5 cm. 

(iii) Mark a point C on this line such that BC = 1 unit. 

(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O. 

(v) With O as center and OC = OA as radius, draw a semicircle. 

(vi) Draw a line BD, which is perpendicular to AB at B. 

(vii) Now BD = \(\sqrt{6.5}\), which can be marked in the number line as the value of BE = BD = \(\sqrt{6.5}\)

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