Question

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

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 ∆ ORQ is obtained by drawing seg OR.
∙ l(OQ) = $\sqrt{2}$, l(QR) = 1

∴ by Pythagoras theorem,
[l(OR)]² = [l(OQ)]² + [l(QR)]²

= $\boxed{0}$² + $\boxed{0}$² = $\boxed{0}$ + $\boxed{0}$

= $\boxed{0}$

∴ l(OR) = $\boxed{0}$

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 line $\sqrt{3}$.

Answer 1

∙ The point Q on the number line shows the number $\underline{\sqrt{2}}$.
∙ 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 ∆ ORQ is obtained by drawing seg OR.
∙ l(OQ) = $\sqrt{2}$, l(QR) = 1
∴ by Pythagoras theorem,
[l(OR)]² = [l(OQ)]² + [l(QR)]²
= ${\boxed{\sqrt{2}}}^2+{\boxed{1}}^2=\boxed{2}+\boxed{1}$
= 3
∴ l(OR) = $\boxed{\sqrt{3}}$
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 line $\sqrt{3}$.