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

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Answer 1 · 2015-07-23T22:01:03

#sqrt(15)/3#

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)#