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What is the square root of 35/36?

1 Answer

Nov 29, 2015

$\frac{\sqrt{35}}{6} \approx 0.9860133$ $sqrt(35)/6 ~~ 0.9860133$

Explanation:

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

So in our case:

$\sqrt{\frac{35}{36}} = \frac{\sqrt{35}}{\sqrt{36}} = \frac{\sqrt{35}}{6}$ $sqrt(35/36) = sqrt(35)/sqrt(36) = sqrt(35)/6$

$\sqrt{35} = \sqrt{5 \cdot 7}$ $sqrt(35) = sqrt(5*7)$ 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 $35$ $35$ is of the form $n^{2} - 1$ $n^2-1$ , its square root does take a simple form as a continued fraction:

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

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