Question

How square root spiral is found ?

Answer 1

I believe you mean something like below
$\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x + ....} } } }$
To solve something like above I am considering below example.
$\sqrt{4 + \sqrt{4 + \sqrt{4 + \sqrt{4 + ....} } } }$
To solve above put
$y = \sqrt{4 + \sqrt{4 + \sqrt{4 + ...} } }$
Which implies
$y = \sqrt{4 + y}$
Square on both sides and solve the quadratic equation below.
${y}^{2} = 4 + y$
This will give you y and the value of 'square root' spiral.
Hope this helps.

Answer 2

Step-by-step explanation:

I believe you mean something like below

\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x + ....} } } }

x+

x+

x+

x+....

To solve something like above I am considering below example.

\sqrt{4 + \sqrt{4 + \sqrt{4 + \sqrt{4 + ....} } } }

4+

4+

4+

4+....

To solve above put

y = \sqrt{4 + \sqrt{4 + \sqrt{4 + ...} } }y=

4+

4+

4+...

Which implies

y = \sqrt{4 + y}y=

4+y

Square on both sides and solve the quadratic equation below.

{y}^{2} = 4 + yy

2

=4+y

This will give you y and the value of 'square root' spiral.

Hope this helps.