How do you evaluate #\sqrt ( ( - 1- 2) ^ ( 2) + ( 2- ( - 4) ^ ( 2) ) )#?

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Answer 1 · 2017-09-14T10:41:45

#sqrt(5) i#

We have: #sqrt((- 1 - 2)^(2) + (2 - (- 4)^(2)))#

Let's evaluate the expressions within the parentheses:

#= sqrt((- 3)^(2) + (2 - 16))#

#= sqrt(9 + (- 14))#

#= sqrt(- 5)#

Then, let's express the number underneath the square root function as a product:

#= sqrt(- 1 times 5)#

Using the rules of surds:

#= sqrt(- 1) times sqrt(5)#

#sqrt(- 1)# is the imaginary unit #i# in mathematics.

#= i times sqrt(5)#

#= sqrt(5) i#