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Question

 Locate \(\sqrt {3}\) on the number line.

Answer

See solution below 
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Solution

Solution for Locate sqrt {3} on the number line.
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 \(\sqrt{3}\).
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