Show how $square root of 5$ can be represented on the number line.

Solution

Representation of

square root of 5

on the number line
Consider a unit square OABC and transfer it onto the number line making sure that the vertex O coincides with zero.
Then OB =

square root of 1 squared plus 1 squared end root equals square root of 2

Construct BD of unit length perpendicular to OB.
Then OD =

square root of open parentheses square root of 2 close parentheses squared plus 1 squared end root space equals space square root of 3

Construct BD of unit length perpendicular to OB.
Then OE =

square root of left parenthesis square root of 3 right parenthesis squared plus 1 squared end root space equals space square root of 4 space equals 2

Construct BD of unit length perpendicular to OB.
Then OF =

square root of 2 squared plus 1 squared end root equals square root of 5

Using a compass, with centre O and radius OF, draw an arc which intersects the number line in the point R. Then R corresponds to

square root of 5.

Representation of

square root of 5.

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