Question

Show the number √7 on the number line.

Answer 1

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 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. Similarly, draw a line CD perpendicular to the number line through the point C such that l(CD) = 1 unit.

By Pythagoras theorem,

l(OD) = √6 units

The point E shows the number √6 .

Similarly, draw a line EP perpendicular to the number line through the point E such that l(EP) = 1 unit.

By Pythagoras theorem,

l(OP) = √7 units

The point F shows the number √7.