How do you simplify $\sqrt{19}$ $sqrt19$ ?

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Answer 1 · 2016-05-16T19:52:44

$\sqrt{19}$ $sqrt(19)$ is already in simplest form.

$19$ $19$ is a prime number, so has no square factors.

As a result it is not possible to simplify $\sqrt{19}$ $sqrt(19)$ , the positive irrational number whose square is $19$ $19$ .

$\sqrt{19} \approx 4.35889894354$ $sqrt(19) ~~ 4.35889894354$

The continued fraction expansion of $\sqrt{19}$ $sqrt(19)$ looks like this:

$sqrt(19) = [4; bar(2, 1, 3, 1, 2, 8)] = 4+1/(2+1/(1+1/(3+1/(1+1/(2+1/(8+1/(2+1/(1+...))))))))$

We can get an economical rational approximation for $sqrt(19)$ by truncating just before the end of the repeating part:

$sqrt(19) ~~ [4; 2, 1, 3, 1, 2] = 4+1/(2+1/(1+1/(3+1/(1+1/2)))) = 170/39 = 4.bar(358974)$

How do you simplify sqrt19√19 sqrt19?