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

= (...)² + (...)² = ... + ...

= ... 

So, l(OR) = ...

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.