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

1 Answer
Sep 2, 2017

Answer:

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

Explanation:

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

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

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using the above principle.

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

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