SOLUTION: Simplify {{{sqrt(-32)}}}

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Question 90036: Simplify

sqrt%28-32%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28-32%29

sqrt%28-1%2A32%29 Factor out a -1

sqrt%28-1%29%2Asqrt%2832%29 Break up the root

i%2Asqrt%2832%29 Replace sqrt%28-1%29 with i

Now lets simplify sqrt%2832%29:

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%2816%2A2%29 Factor 32 into 16*2

sqrt%2816%29%2Asqrt%282%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

4%2Asqrt%282%29 Take the square root of the perfect square 16 to get 4

So the expression sqrt%2832%29 simplifies to 4%2Asqrt%282%29


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Answer:
So sqrt%28-32%29 simplifies to 4%2Ai%2Asqrt%282%29