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Question

Locate \(\sqrt {2}\) on the number line.

Answer

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Solution

Given, \(\sqrt {2}\)
Solution:
We have, \(\sqrt {2}\)
Consider a unit square \(OABC\), with each side \(1\ unit\) in length, which is shown as below:
Solution for Locate sqrt {2} on the number line.
Now, using Pythagoras theorem in \(\Delta OAB,\) we get,
\((Hypotenuse)^2=(Perpendicular)^2+(Base)^2\)
\(\Rightarrow\ OB^2=AB^2+OA^2\)
\(\Rightarrow\ OB^2=1^2+1^2\)
\(\Rightarrow\ OB==\sqrt{1^{2}+1^{2}}=\sqrt{2} \)
Using a compass with centre \(O\) and radius \(OB,\) draw an arc intersecting the number line at the point \(P\).
Thus, \(P\) corresponds to \(\sqrt{2}\) on the number line.
Solution for Locate sqrt {2} on the number line.
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