# 1)Write 3 numbers whose decimal expansion are non terminating and non recurring?? 2)Represent root 10,root 6 on a number line.

1
by Rajutty

2015-04-17T12:40:06+05:30
1)
the problem is simply asking for you to list 3 'irrational' numbers.
since the square root of any number that is not a perfect square is irrational, you can list some like:
√2, √3, √5
but π also works, as well as ∛2, ∛4, and the fifth root of 16.

2)
Take a point O representing 0 on a number line.
With some suitable scale (say 1 inch) mark a point P which represents 1 on the number line.
At P darw a line PQ perpendicular to the number line such that PQ = 1.
Join O to Q.
=> OQ = √2.
With O as center and radius = √2, cut an arc at R on the number line.
=> OR = √2.
Now, draw a line RS = 1 perpendicular to the number line.
Join O to S.
=> OS = √3
With O as center and radius = OS cut an arc at T on the number line
=> OT = √3
You can continue like this and get √4, √5, √6, .... √10 and so on on the number line.

Specifically for √10, mark a point A on the number line such that OA = 3 and draw a line AB perpendicular to the number line such that AB = 1
=> OB = √10 (by pythagorus theorem)
With center at O and radius = OB = √10, cut an arc at C on the number line
=> OC = √10.