Question

Locate `sqrt(5), sqrt(10)` and `sqrt(17)` on the number line.

Answer 1

`sqrt(5)` on the number line:

5 can be written as the sum of the square of two natural numbers:

i.e., 5 = 1 + 4 = 1² + 2²

On the number line,

Take OA = 2 units.

Perpendicular to OA, draw BA = 1 unit.

Join OB.

Using the Pythagoras theorem,

We have, OB = `sqrt(5)`

Draw an arc with centre O and radius OB using a compass such that it intersects the number line at the point C.

Then, we get, C corresponds to `sqrt(5)`.

Or we can say that OC = `sqrt(5)`

`sqrt(10)` on the number line:

10 can be written as the sum of the square of two natural numbers:

i.e., 10 = 1 + 9 = 1² + 3²

On the number line,

Take OA = 3 units.

Perpendicular to OA, draw BA = 1 unit.

Join OB.

Using the Pythagoras theorem,

We have, OB = `sqrt(10)`

Draw an arc with centre O and radius OB using a compass such that it intersects the number line at the point C.

Then, the point C corresponds to `sqrt(10)`.

Or we can say that OC = `sqrt(10)`

`sqrt(17)` on the number line:

17 can be written as the sum of the square of two natural numbers:

i.e., 17 = 1 + 16 = 1² + 4²

On the number line,

Take OA = 4 units.

Perpendicular to OA, draw BA = 1 unit.

Join OB.

Using the Pythagoras theorem,

We have, OB = `sqrt(17)`

Draw an arc with centre O and radius OB using a compass such that it intersects the number line at the point C.

Then, point C corresponds to `sqrt(17)`.

Or, we can say that OC = `sqrt(17)`