What is the simplest radical form for $sqrt(145)$ ?

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Answer 1 · 2017-03-28T20:56:21

$sqrt145$

There is no simple form for this.

Let's try using the factors of $145$

$sqrt145=sqrt145*sqrt1$

$sqrt145=sqrt29*sqrt5$

This cannot be broken into any simpler forms so there is no simple from for $sqrt145$

Answer 2 · 2017-03-28T21:03:28

$sqrt(145)$

The prime factorisation of $145$ is:

$145 = 5*29$

Since this has no square factors, there is no simpler radical form than $sqrt(145)$ .

Note however that $145 = 12^2+1$ is of the form $n^2+1$

As a result, its square root has a very simple form as a continued fraction:

$sqrt(145) = [12;bar(24)] = 12+1/(24+1/(24+1/(24+1/(24+1/(24+...)))))$

What is the simplest radical form for sqrt(145)sqrt(145)?