How do you evaluate #\sqrt { - 18} ( \sqrt { - 7} - \sqrt { 3} )#?

1 Answer
Rachel
Apr 27, 2017

#3sqrt(14)-3isqrt(6)#

Explanation:

#sqrt(-18)(sqrt(-7)-sqrt(3))#

Let's convert the #sqrt(color(black)(x))# to #color(black)(x)^(1/2)#. This doesn't change anything, but I like to work with exponents instead of roots. The rules are more obvious for exponents:
#(-18)^(1/2)((-7)^(1/2)-(3)^(1/2))#

distribute the #(-18)^(1/2)#

#color(red)((-18)^(1/2))xx(-7)^(1/2)-(color(red)((-18)^(1/2))xx3^(1/2))#

Simplify

#(126)^(1/2)-(-54)^(1/2)#

#sqrt(126)-sqrt(-54)#

We cannot combine square roots that have different radicands, so we just simplify the individual square roots

#sqrt(3*3*14)-sqrt(-1*3*3*6)#

#3sqrt(14)-3isqrt(6)#

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