How to represent square root of 10 on the number line?

Question

How to represent the points corresponding to square roots of non-perfect squares? (e.g. square root of 2,3,5,6,etc)

give step by step method or suggest any link on the web which i can follow

Answer 1

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.

Answer 2

root 10 is 3.162278

It's a point between 3 and 4

between 3.1 and 3.2

between 3.16 and 3.17

etc

.

Answer 3

Well, the method is not actually to approximate the values and mark it on a number line. There is a separate method for performing this task. Visit this link:

http://en.wikipedia.org/wiki/Spiral_of_T...

That's how I learned last year, in my 9th Grade........

Answer 4

I guess the obvious answer is represent them on the real number line. The square root of 10, for example, is approximately 3.16, so place a dot about three 20ths of the way from 3 towards 4.

If you want to be a smart-***, you could always use a tricky square scale, and just represent all square roots evenly spaced (like you would normally represent integers).

EDIT: Judging by my approval rating, I obviously missed whatever it was you wanted to know. I suggest you add some details to your question so that we know exactly what that is.