How do you simplify $sqrt(-2156)$ ?

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Answer 1 · 2018-04-04T08:53:27

$46.43i$

$sqrt(-2156) = sqrt(-1) * sqrt(2156)$

$i^2 = -1 " or " i = sqrt(-1)$

$i * sqrt2156 ~~ i * 46.43 ~~ 46.43 i$

Answer 2 · 2018-04-04T10:37:58

$sqrt(-2156) = 14sqrt(11)i$

The prime factorisation of $2156$ is:

$2156 = 2^2 * 7^2 * 11$

Hence:

$sqrt(2156) = sqrt(14^2 * 11) = 14sqrt(11)$

and:

$sqrt(-2156) = sqrt(2156) i = 14sqrt(11)i$

How do you simplify sqrt(-2156)sqrt(-2156)?