SOLUTION: Simplify the following expression. {{{sqrt (-98) sqrt (-50) }}}

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Question 373662: Simplify the following expression.
sqrt+%28-98%29+sqrt+%28-50%29+
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28-98%29%2Asqrt%28-50%29
Since we have negative radicands (expressions within a radical) of an even numbered root (square roots are 2nd roots), we start by factoring out -1:
sqrt%28-1%2A98%29%2Asqrt%28-1%2A50%29
Then we use a property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29, to separate the -1 factors into their own square roots:
sqrt%28-1%29%2Asqrt%2898%29%2Asqrt%28-1%29%2Asqrt%2850%29
Since sqrt%28-1%29+=+i this becomes:
i%2Asqrt%2898%29%2Ai%2Asqrt%2850%29
We could multiply out the remaining square roots. But instead of multiply 98*50, I am going to simplify the square roots before I multiply them:
i%2Asqrt%2849%2A2%29%2Ai%2Asqrt%2825%2A2%29
i%2Asqrt%2849%29%2Asqrt%282%29%2Ai%2Asqrt%2825%29%2Asqrt%282%29
Since sqrt%2849%29+=+7 and sqrt%2825%29+=+5 this becomes:
i%2A7%2Asqrt%282%29%2Ai%2A5%2Asqrt%282%29
Since this is all multiplication, the Commutative and Associative Properties apply. So we can rearrange the order and rearrange the grouping in any ways we choose:
7%2A5%2A%28sqrt%282%29%2Asqrt%282%29%29%2A%28i%2Ai%29
Since sqrt%282%29%2Asqrt%282%29+=+2 (by definition), this becomes:
7*5*2*(i*i)
Since i%2Ai=i%5E2=-1 we get:
7*5*2*(-1)
Multiplying these numbers we get:
-70