SOLUTION: Simplify the following expression. square root of -6 and -42. Both numbers are next to each other with the square root sign in front of each number.

Question 609671: Simplify the following expression.
square root of -6 and -42. Both numbers are next to each other with the square root sign in front of each number.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

When the radicand (the number inside) of a square root is negative, then the number is what is called an imaginary number. When working with imaginary numbers the first thing to do is to rewrite them in terms of "i":
and

Rewriting your numbers in terms of i. Start by factoring out -1 in each radicand:

Use a property of radicals, , to split the factors into separate square roots:

Replace with "i":

Now we can proceed with "normal" simplification. Using the Commutative and Associative Properties to rearrange the order and the grouping:

Multiplying:

Replacing with -1:

Simplifying the square root:

This is the simplified expression.
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