Using the concept we saw in the previous video,
let's see how we plot the length root 2 on a number line.
So let's plot it on this number line.
We need to make a right triangle with one unit as the base.
Let 'OA' be the base of that triangle.
We also want its height to be one unit long.
Let's draw the height 'AB' like this.
We just drew 'AB' equal to one unit
perpendicular to 'OA'.
Both these lengths equal one unit .
Now all we have to do is join 'OB' like this.
Let's analyze the figure!
We have 'OA' equal to one unit, and 'AB' equal to one unit.
Using the Pythagoras theorem,
we have 'OB squared' equal to 'OA squared' plus 'AB squared'.
That would equal 1 squared, plus 1 squared which is 2.
Taking the Square root on both sides we get 'OB' equal to root 2 units.
This length here will be root 2 units.
We just need this length here on the number line.
To do that, we keep the vertex of the compass here
and with length, 'OB' cut an arc on the number line.
Let's call this point 'C'.
This green length 'OC' will equal this length,
since the other radii of the same circle.
Hence length 'OC' is also equal to root 2.
And if we need 'minus root 2',
then we cut the same arc on the other side of 'O'.
Let's quickly see how we can actually construct it.
Let 'OA' be one unit long. Then we take a protractor
make a 90-degree mark and join that point to 'A'.
Then on the compass, we take the length of one unit
and mark it on this line to get  'AB' as one unit .
And then we join, 'OB'.
This length 'OB' is root two units. And that is the length
we need on the number line.
So we keep the compass on point O, take length 'OB' and cut an arc like this.
That gives us length 'OC' as root 2 units.
