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.

$= i times sqrt(5)$

$= sqrt(5) i$

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