Question

The number √2 is shown on a number line. Steps are given to show √3 on the number line using √2. Fill in the boxes properly and complete the activity.

The point Q on the number line shows the number ……….

A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.

Right angled ∆OQR is obtained by drawing seg OR. l(OQ) = √2, l(QR) = 1

∴By Pythagoras theorem,

[l(OR)]² = [l(OQ)]² + [l(QR)]²

Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number √3

Answer 1

The point Q on the number line shows the number √2.

A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.

Right angled ∆OQR is obtained by drawing seg OR. l(OQ) = √2, l(QR) = 1

∴By Pythagoras theorem, 

[l(OR)]² = [l(OQ)]² + [l(QR)]²

.. .[Taking square root of both sides]

Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number √3.