Question

How do you simplify `(7sqrt(-3))(2sqrt(-27))`?

Answer 1

Always deal with imaginary numbers first. Final answer: `-126`

Explanation:

If you ignore the rule of imaginary numbers which states that `sqrt(-1)=``i` and `i^2`=-1, you would be tempted to multiply all terms together to get `14sqrt(81)=14*9=126` ... which would be incorrect.

To keep the validity of the complex number system, always deal with the imaginary part first. To do this, rewrite the equation:

`(7sqrt(3)*sqrt(-1))(2sqrt(27)*sqrt(-1))=(sqrt(-1)*sqrt(-1))(7sqrt(3)*2sqrt(27))`

Now you can multiply terms within the parentheses.

`(sqrt(-1)*sqrt(-1))=i*i=i^2=-1`

and

`(7sqrt(3)*2sqrt(27))=14sqrt(81)=14*9=126`

Multiply these together and you get `126*-1=-126`