Answer: 12i*sqrt(2)
where i = sqrt(-1)
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Step-by-step explanation:
The goal is to find the largest perfect square factor so we can then use the rules shown below
- sqrt(xy) = sqrt(x)*sqrt(y)
- sqrt(x^2) = x where x is nonnegative
So we have these steps
sqrt(-288) = sqrt(-1*144*2)
sqrt(-288) = sqrt(-1)*sqrt(144)*sqrt(2) .... use rule 1 above
sqrt(-288) = i*12*sqrt(2) ... use rule 2 and i = sqrt(-1)
sqrt(-288) = 12i*sqrt(2)