Question

Represent root 6, root 7 and root 8 on the number line.

Answer 1

You can represent roots of non perfect squares using pythagorean theorem.

For √6:
Draw a number line.
Take two units on the number line from 0. It reaches 2.
From 2 take 1 unit perpendicular to the number line.
Join 0 and the end point of the 1 unit which is perpendicular to the number line.
This is the hypotenuse.
Now if you calculate you find out that the value of hypotenuse is √5.
Now, take √5 as base and draw 1 unit perpendicular to the base on the end point other than 0.
Join 0 and the end point of the 1 unit which is perpendicular to the base.
This is hypotenuse.
Now if you calculate you find out that the value of hypotenuse is √6.
Draw an arc with centre as O and radius as the √6 hypotenuse and intersecting the number line.
This is √6 on number line.

For √7:
As you have already marked √6 on number line, take the √6 on number line as the base.
Draw 1 unit perpendicular to the number line.
Join 0 and the end point of the 1 unit perpendicular to the number line.
This is the hypotenuse.
Now if you calculate you find out that the value of hypotenuse is √7.  
Draw an arc with centre as O and radius as the √7 hypotenuse and intersecting the number line.
This is √7 on number line.

For √8:
As you have already marked √7 on number line, take the √7 on number line as the base.
Draw 1 unit perpendicular to the number line.
Join 0 and the end point of the 1 unit perpendicular to the number line.
This is the hypotenuse.
Now if you calculate you find out that the value of hypotenuse is √8.  
Draw an arc with centre as O and radius as the √8 hypotenuse and intersecting the number line.
This is √8 on number line.

Hope my answer helps you..