Simplify the radical when the radicand contains a fraction

Question

Radical: sqrt 2/3

Radicand: 2/3

Answer 1

In this case, you want to take the square root of both the top and the bottom, then simplify so that there is only a square root on the top. Here are the steps, in detail:

sqrt(2/3) = sqrt(2)/sqrt(3)

Now we want to get rid of the square root (radical) on the bottom, so we multiply both the top and the bottom by sqrt(3):

=sqrt(2)*sqrt(3) / sqrt(3)*sqrt(3)

Note: when multiplying square roots, you can multiply the insides and put them under a radical

=Sqrt(6)/sqrt(9)

= sqrt(6)/3

Hope this helps!

Answer 2

√(2/3)

√2 / √3

√2 / √3)(√3 / √3)

√6 / 3