How do you evaluate 3\sqrt { - 24} * 2\sqrt { - 18}?

1 Answer
May 11, 2017

Use i=sqrt(-1) and then simplify. Answer: -72sqrt(3)

Explanation:

Original question: Evaluate 3sqrt(-24)*2sqrt(-18)

Since we cannot square root a negative (we CANNOT simply multiplying the square roots together to make the number inside the square root positive), we use the imaginary unit i=sqrt(-1) to denote the imaginary unit:

3sqrt(-24)*2sqrt(-18)
=3isqrt(24)*2isqrt(18)
=6i^2sqrt(24*18)
=6i^2sqrt(2^3*3*2*3^2)
=6i^2sqrt(2^4*3^3)
=6i^2*2^2*3sqrt(3)

Note that i^2=-1
=-72sqrt(3)