# What is the square root of 35/36?

Nov 29, 2015

$\frac{\sqrt{35}}{6} \approx 0.9860133$

#### Explanation:

If $a , b > 0$ then $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

So in our case:

$\sqrt{\frac{35}{36}} = \frac{\sqrt{35}}{\sqrt{36}} = \frac{\sqrt{35}}{6}$

$\sqrt{35} = \sqrt{5 \cdot 7}$ cannot be further simplified since it has no square factors.

It is an irrational number, so cannot be expressed as a repeating decimal or ratio of whole numbers.

Since $35$ is of the form ${n}^{2} - 1$, its square root does take a simple form as a continued fraction:

sqrt(35) = [5;bar(1, 10)] = 5+1/(1+1/(10+1/(1+1/(10+...))))