Question 1128382
<font color="black" face="times" size="3">Use these rules
Rule 1: {{{i = sqrt(-1)}}} by definition
Rule 2: {{{sqrt(x*y) = sqrt(x)*sqrt(y)}}}
Rule 3: {{{sqrt(x^2) = x}}} where x is nonnegative


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{{{2*sqrt(-81) - 2*sqrt(-100) = 2*sqrt(-1*81) - 2*sqrt(-1*100)}}}


{{{2*sqrt(-81) - 2*sqrt(-100) = 2*sqrt(-1)*sqrt(81) - 2*sqrt(-1)*sqrt(100)}}} Use rule 2


{{{2*sqrt(-81) - 2*sqrt(-100) = 2*sqrt(-1)*sqrt(9^2) - 2*sqrt(-1)*sqrt(10^2)}}}


{{{2*sqrt(-81) - 2*sqrt(-100) = 2*i*sqrt(9^2) - 2*i*sqrt(10^2)}}} Use rule 1


{{{2*sqrt(-81) - 2*sqrt(-100) = 2*i*9 - 2*i*10}}} Use rule 3


{{{2*sqrt(-81) - 2*sqrt(-100) = 18i - 20i}}}


{{{2*sqrt(-81) - 2*sqrt(-100) = -2i}}}


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Answer: <b><font size=5 color=red>-2i</font></b></font>