How do you simplify: the square root of -175 ?

Question

2865 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-22T15:24:49

$5i*sqrt(7)$

Factor the number to primes:

$sqrt(-125)=sqrt(-1*5*5*7)$

Pull out the duplicate 5 and $i$ :
$sqrt(-1*5*5*7)=5i*sqrt(7)$

Answer 2 · 2015-07-22T15:26:33

$sqrt(-175) = 5sqrt(7)i$

$sqrt(-175) = sqrt(175)*sqrt(-1)$

$color(white)("XXXX")$ $= sqrt(175)i$

$color(white)("XXXX")$ $= sqrt(5^2*7)i$

$color(white)("XXXX")$ $= 5sqrt(7)i$