What is the simplified expression for radical 12 minus 3 radical 3?

Answer 1

In order to work with radicals (adding or subtracting) they have to have the same radical expression.

ex: 2 rad 3 + 4 rad 3 = 6 rad 3.

If it helps, change the similar radicals to a variable.

2 rad 3 + 4 rad 3

2 x + 4 x = 6x

and then substitute your radical back in for the variable.

6 rad 3

---- rad 12 - 3 rad 3

Let's simplify radical 12. First, factor 12 into a perfect square, and a not perfect square.)

Hint: we want it to be radical 3 to work with it... 3 times what is 12?

rad 12 = sqrt(12) = sqrt(4*3)

sqrt(4*3) = sqrt(4)*sqrt(3)

sqrt(4) is just 2! We bring this to the "outside" of the radical.

sqrt(4)*sqrt(3) = 2 sqrt(3) or 2 rad 3

rad 12 - 3 rad 3

2 rad 3 - 3 rad 3

(or 2x - 3x if it helps)

We're left with: -1 rad 3, or just - rad 3 (negative radical 3)