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

##### 2 Answers
Mar 28, 2017

$\sqrt{145}$

#### Explanation:

There is no simple form for this.

Let's try using the factors of $145$

$\sqrt{145} = \sqrt{145} \cdot \sqrt{1}$

$\sqrt{145} = \sqrt{29} \cdot \sqrt{5}$

This cannot be broken into any simpler forms so there is no simple from for $\sqrt{145}$

Mar 28, 2017

$\sqrt{145}$

#### Explanation:

The prime factorisation of $145$ is:

$145 = 5 \cdot 29$

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+...)))))