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

Question 373662: Simplify the following expression.

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

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:

Then we use a property of radicals, , to separate the -1 factors into their own square roots:

Since this becomes:

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:

Since and this becomes:

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:

Since (by definition), this becomes:
7*5*2*(i*i)
Since we get:
7*5*2*(-1)
Multiplying these numbers we get:
-70
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