How do you simplify #(8+sqrt(-18)) - (4+3sqrt(2) )#?

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Answer 1 · 2017-09-02T14:03:45

#4+3sqrt(2)(i-1)#

Before we start note that: #sqrt(-1)=i#

Write as: #8-4+sqrt((-1)xx(+18))-3sqrt2#

#4+sqrt(2xx3^2xx(-1))-3sqrt2#

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Using simple numbers to demonstrate a point

#sqrt16=sqrt(2^2xx2^2) =sqrt(2^2)xxsqrt(2^2)=4#

So you can 'split' the contents of a root.
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Using the above principle.

#4+3sqrt(2)sqrt(-1)-3sqrt(2)#

#4+3sqrt(2)(i-1)#