Thread: Converting irrational number to surd form

I have the following function:

where

Say I solve this for y, and I get the solution 1.73205

I happen to know this is , but if I didn't, is there an intuitive way to make this connection? It seems to be bad form to express it as a decimal.

Thanks.

Hello, Glitch!

I have the following function:
. .
where

Say I solve this for , and I get the solution 1.73205

I happen to know this is ,
but if I didn't, is there an intuitive way to make this connection?
It seems to be bad form to express it as a decimal.

We're expected to know about the 30-60 right triangle.

Code:

                              *
                          * 60*
                2     *       *
                  *           * 1
              *               *
          * 30                *
      *   *   *   * _ *   *   *
                   √3

Hence, we have: .


So we have: .

Ahh, I had forgotten about that triangle! Thanks.