How do I solve $sqrt(-8)(sqrt(-3)-sqrt(5))$ ?

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Answer 1 · 2016-11-21T04:52:23

$-2sqrt(6)-(2sqrt10)i$
or
$-2sqrt2(sqrt3+isqrt5)$

"Simplify" is perhaps a better word than "solve", since there's no variable to solve for. First, we rewrite using $i$ notation:

$sqrt(-8)(sqrt(-3)-sqrt5)$

$=isqrt8(isqrt3-sqrt5)$

$=2isqrt2(isqrt3-sqrt5)$

Next, distribute:

$=2i^2sqrt6-2isqrt10$

Then, we remember that $i^2=-1$ by definition, so we can write

$=-2sqrt(6)-(2sqrt10)i$

This is now in $x+yi$ form. It can be "simplified" further, however, by factoring out - $2sqrt2$ from both terms:

$=-2sqrt2(sqrt3+isqrt5)$

How do I solve sqrt(-8)(sqrt(-3)-sqrt(5))sqrt(-8)(sqrt(-3)-sqrt(5))?