Question 90036
{{{sqrt(-32)}}}


{{{sqrt(-1*32)}}} Factor out a -1


{{{sqrt(-1)*sqrt(32)}}} Break up the root


{{{i*sqrt(32)}}}  Replace {{{sqrt(-1)}}} with i


Now lets simplify {{{sqrt(32)}}}:


So let's list the factors of 32

Factors:

1, 2, 4, 8, 16, 32



Notice how 16 is the largest perfect square, so lets factor 32 into 16*2



{{{sqrt(16*2)}}} Factor 32 into 16*2
 
{{{sqrt(16)*sqrt(2)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{4*sqrt(2)}}} Take the square root of the perfect square 16 to get 4 
 
So the expression {{{sqrt(32)}}} simplifies to {{{4*sqrt(2)}}}



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Answer:

So  {{{sqrt(-32)}}} simplifies to {{{4*i*sqrt(2)}}}