SOLUTION: Simplify -2√180u³v^6 I know what the answer is but I don't understand the u³ and how is breaks down because 2 doesn't go in evenly to the exponent 3? If you pull a "u" out a

Question 1201014: Simplify -2√180u³v^6
I know what the answer is but I don't understand the u³ and how is breaks down because 2 doesn't go in evenly to the exponent 3? If you pull a "u" out and leave one under the square root, you have a 1 "u" left over. Where is it? What am I missing?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have a u^3 under the dequare root sign.
you can pull out a u^2 and you have to leave a u under the squar root sign.
with the v^6, you can pull out 3 v^2.
the result is -2 * u * v^3 * sqrt(180 * u)
the sqrt(180) becomes sqrt(3 * 3 * 20), so you can pull out a 3 to get:
-2 * u * v^3 * 3 * sqrt(20 * u)
this simplifies to -6 * u * v^3 * sqrt(20 * u).
you can test to see if you did this correctly by randomly assigning a value fo u and v.
i chose 3 for u and 5 for v.
the original expression becomes -2 * sqrt(180 * 3^3 * 5^6) which results in - 17428.42506.
the final expression becomes -6 * 3 * 5^3 * sqrt(20 * 3) = -17428.42506.
the answers are the same which incidcates that the simplification is correct.

note that 20 is equal to 2 * 2 * 5, so that can also be simplified a little further to get:
-6 * u * v^3 * sqrt(2 * 2 * 5 * u) which becomes:
-6 * 2 * u * v^3 * sqrt(5 * u) which becomes:
-12 * u * v^3 * sqrt(5 * u).
using u = 3 and v = 5, i get -17428.42506, indicating the simplification is still good.

let me know if this explains what you were asking and if you have any further quetions.
theo
Answer by greenestamps(13196) (Show Source): You can put this solution on YOUR website!

Break the radicand into factors, of which as many as possible are perfect squares:

Take the perfect square factors outside the radical, leaving the other factors in the radicand:

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