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1)Write 3 numbers whose decimal expansion are non terminating and non recurring??

2)Represent root 10,root 6 on a number line.

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by Rajutty

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2)Represent root 10,root 6 on a number line.

by Rajutty

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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.