Show how \(\sqrt {5}\) can be represented on the number line.

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Firstly, draw a line segment \(AB\) of length \(2\) unit on the number line.

Then draw a perpendicular line segment \((BC)\) at point \(B\) of \(1\) unit.

Then join the points \(\mathrm{C}\) and \(\mathrm{A}\), to form a line segment \((AC).\)

According to Pythagoras Theorem,

\(\Rightarrow A C^{2}=A B^{2}+B C^{2}\)

\(\Rightarrow A C^{2}=2^{2}+1^{2}\)

\(\Rightarrow A C=\sqrt{2^{2}+1^{2}}\)

\(\Rightarrow A C=\sqrt{5}\)

Now, draw the arc \((ACD)\), to get the number on the number line.

Then draw a perpendicular line segment \((BC)\) at point \(B\) of \(1\) unit.

Then join the points \(\mathrm{C}\) and \(\mathrm{A}\), to form a line segment \((AC).\)

According to Pythagoras Theorem,

\(\Rightarrow A C^{2}=A B^{2}+B C^{2}\)

\(\Rightarrow A C^{2}=2^{2}+1^{2}\)

\(\Rightarrow A C=\sqrt{2^{2}+1^{2}}\)

\(\Rightarrow A C=\sqrt{5}\)

Now, draw the arc \((ACD)\), to get the number on the number line.

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