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

1 Answer
Y
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)#

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