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## QuestionMathsClass 9

Locate $$\sqrt {2}$$ on the number line.

See the analysis below
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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:

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.