#### 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 `

= _____^{2} + _____^{2} = _____ + _____

= ______

∴ 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.

#### Solution

- 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 ∆ ORQ 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} + 1^{2} = 2 + 1

= 3

∴ l(OR) = √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 √3 .

Is there an error in this question or solution?

Solution 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. Concept: To Show Rational Numbers on a Number Line.