express in simplest radical form

[Chocolate]

this problem has to be done without using a calculator and work has to be shown:

(sq. root 12)/((2 sq. root3)-4)

plz help me!

 

[Erik_D]

For (sq. root 12)/((2 sq. root3)-4)

break up the 12 ; sqrt(4*3)/((2sqrt3)-4)

remove the 4 from the radical ; (2sqrt3)/((2sqrt3)-4)

factor a 2 out of the bottom ; (2sqrt3)/(2(sqrt3-2)

cancel out the 2s ; (sqrt3)/(sqrt3-2)

multiply by (sqrt3+2)/(sqrt3+2) to get the radical out of the bottom ; (sqrt3*(sqrt3+2))/((sqrt3-2)(sqrt3+2))

multiply the factors in the top ; (3+2sqrt3)/((sqrt3-2)(sqrt3+2))

multiply the factors in the bottom ; (3+2sqrt3)/(3-4)

subtract the numbers in the bottom ; (3+2sqrt3)/(-1)

bring the negative up front ; -(3+2sqrt3)/(1)

divide by 1 ; -(3+2sqrt3)

distribute the negative ; -3-2sqrt3

That's it.

 

[Chocolate]

Thanks! it all makes sense now, but if i didn't get any help, i would've never been able to work it out myself.