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## QuestionMathsClass 9

Locate $$\sqrt {3}$$ on the number line.

See solution below
4.6
4.6

## Solution

Draw a number line with $$0$$ at O.
Construct $$OA$$ of unit length along $$x$$ axis in the positive direction. Then draw $$AB$$ of unit length perpendicular to $$OA$$. Now $$OB's$$ length is $$=\sqrt{1^2+1^2}=\sqrt2$$[By Pythagoras theorem]
Construct BD of unit length perpendicular to OB (as in figure). By using the Pythagoras theorem, we see that OD $$=\sqrt{(\sqrt{2})^{2}+1^{2}}=\sqrt{3}$$. With the help of a compass, with centre $$\mathrm{O}$$ and radius $$\mathrm{OD},$$ draw an arc which intersects the number line at the point $$\mathrm{Q}$$. Then Q corresponds to $$\sqrt{3}$$.