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Show the number √5 on the number line.

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Draw a number line and take a point Q at 2 such that l(OQ) = 2 units.

Draw a line QR perpendicular to the number line through the point Q such that l(QR) = 1 unit. Draw seg g OR.

∆OQR formed is a right angled triangle. By Pythagoras theorem,

[l(OR)]2 = [l(OQ)]2 + [l(QR)]2

= 22 + 12

= 4 + 1

= 5

∴l(OR) = √5 units

…[Taking square root of both sides]

Draw an arc with centre O and radius OR. Mark the point of intersection of the number line and arc as C. The point C shows the number √5.

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