What is the simplest radical form of #sqrt(10/6)#?

1 Answer
Jul 23, 2015

Answer:

#sqrt(15)/3#

Explanation:

To get the simplest radical form of #sqrt(10/6)#, you first have to simplify the fraction that's under the radical, #10/6#.

#10/6 = (cancel(2) * 5)/(cancel(2) * 3) = 5/3#

The radical expression becomes

#sqrt(5/3)#

You can go further and write this as

#sqrt(5/3) = sqrt(5)/sqrt(3)#

Rationalize the denominator by multiplying the numerator and the denominator by #sqrt(3)# to get

#(sqrt(5) * sqrt(3))/(sqrt(3) * sqrt(3)) = sqrt(5 * 3)/sqrt(3 * 3) = color(green)(sqrt(15)/3)#