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Question

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

Answer

See solution below
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Solution

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.
Solution for Show how sqrt {5} can be represented on the number line.
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