Question

How do you simplify `asqrt27-2sqrt(3a^2)`?

Answer 1

If `a in RR` then `asqrt(27)-2sqrt(3a^2)=(3a-2abs(a))sqrt(3)`

If `a>=0` then `asqrt(27)-2sqrt(3a^2)=asqrt(3)`

Explanation:

Assuming `a` is a Real number:

`asqrt(27)-2sqrt(3a^2)`

`=asqrt(3^2*3)-2sqrt(a^2*3)`

`=asqrt(3^2)sqrt(3)-2sqrt(a^2)sqrt(3)`

`=(3a-2abs(a))sqrt(3)`

If in addition `a>=0` then `3a-2abs(a) = 3a-2a=a` and

`asqrt(27)-2sqrt(3a^2) = asqrt(3)`