How do you simplify $sqrt 2 / sqrt 10$ ?

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Answer 1 · 2015-10-03T08:47:42

$sqrt(2)/sqrt(10) = sqrt(5)/5$

If $a, b >= 0$ then $sqrt(a/b) = sqrt(a)/sqrt(b)$

$sqrt(2)/sqrt(10) = sqrt(2/10) = sqrt(1/5) = sqrt(5/25) = sqrt(5)/sqrt(25) = sqrt(5)/5$

Notice that I chose to make the denominator a perfect square $25$ in order that the final result has a rational denominator.

How do you simplify sqrt 2 / sqrt 10sqrt 2 / sqrt 10?