How do you simplify #(2+ \sqrt { - 25} ) + ( - 8- \sqrt { - 9} )#?

2 Answers
sankarankalyanam
Jul 25, 2018

#color(purple)(=> -6 + 2i#

Explanation:

#(2 + sqrt-25 ) + (-8 - sqrt(-9)#

#=> (2 + sqrt (25 i^2) ) + (-8 - sqrt(9 i^2)), " as " i^2 = -1#

#=> (2 + 5i) + (-8 - 3i)#

#=> (2 - 8) + (5i - 3i)#

#color(purple)(=> -6 + 2i#

Jim G.
Jul 25, 2018

#-6+2i#

Explanation:

#"note that "sqrt(-1)=i#

#•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)#

#sqrt(-25)=sqrt(25xx-1)=sqrt25xxsqrt(-1)=5i#

#sqrt(-9)=sqrt(9xx-1)=sqrt9xxsqrt(-1)=3i#

#2+sqrt(-25)-8-sqrt(-9)#

#=2+5i-8-3i#

#=(2-8)+(5i-3i)#

#=-6+2i#

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