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

1 Answer
Oct 3, 2015

Answer:

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

Explanation:

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.