Question

The number `sqrt2` is shown on a number line. Steps are given to show `sqrt3` on the number line using `sqrt2`. 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") = sqrt2` ,    `l("QR") = 1`

`therefore` by Pythagoras theorem,

`[l("OR")]^2  = [l("OQ")]^2 + [l("QR")]^2 `

= `square^2`+ `square^2` = `square` + `square`

= `square`

∴ l(OR) = `square`

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 `sqrt3`.

Answer 1

•  The point Q on the number line shows the number `bb\underlinesqrt2`.
• 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) = `sqrt2` , l(QR) = 1

∴ by pythagoras theorem,

[l(OR)]² = [l(OQ)]² + [l(QR)]²

= `bbsqrt2^2 + bb1^2 = bb2 + bb1`

= 3

∴ l(OR) = `bbsqrt2`

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 `sqrt3`.