# Is the square root of 13 a rational number?

Aug 11, 2016

$\sqrt{13} \text{ is an irrational number.}$

#### Explanation:

No, $\sqrt{13}$ is an infinite non-recurring decimal. 13 is not a perfect square and therefore does not have an exact square root.

It is an irrational number, along with numbers such as $\pi , \sqrt{20} , \sqrt{33} , \sqrt{8} , e , e t c$

$\sqrt{13}$ cannot be written as a ratio of integers and as a result cannot be written as a fraction, which is the definition of a rational number.

Rational numbers include the Integers (positive and negative whole numbers) the fractions, and all the terminating and recurring decimals.

$\frac{3}{4} , - 26 , \frac{11}{3} , \frac{2}{9} , 3 \frac{5}{8} , - 204 , e t c$