SOLUTION: what is square root of 4x squared menus 20x plus 25 and three root of negative 8n to the 12 y to the 9 i don't understand how to even start these

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Question 116821: what is square root of 4x squared menus 20x plus 25
and three root of negative 8n to the 12 y to the 9
i don't understand how to even start these
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Your expressions have a little bit of ambiguity in them, but I think you mean:

1) sqrt%284x%5E2-20x%2B25%29 and
2) root%283%2C-8n%5E12+%28y%5E9%29%29


1) if you factor 4x%5E2-20x%2B25 you get %282x-5%29%282x-5%29 (I'll leave it as an exercise for you to verify that is true - Hint: use FOIL). Since %282x-5%29%282x-5%29=%282x-5%29%5E2, we can say:

sqrt%284x%5E2-20x%2B25%29=sqrt%28%282x-5%29%5E2%29=2x-5

2) Again, let's factor the expression under the radical. I'm not going to factor it completely, just enough to make it convenient to take the cube root.

(we can say this because we know that %28x%5Ea%29%28x%5Eb%29=x%5E%28a%2Bb%29)

So, we want

There are three factors of -2, so we take one of them,
There are three factors of n%5E4, so we take one of them,
and there are three factors of y%5E3, so we take one of them, and put them all together:

root%283%2C-8n%5E12+%28y%5E9%29%29=-2n%5E4%28y%5E3%29

And you can multiply %28-2n%5E4%28y%5E3%29%29%28-2n%5E4%28y%5E3%29%29%28-2n%5E4%28y%5E3%29%29 and verify that it equals -8n%5E12+%28y%5E9%29%29 to check the answer.

Hope this helps
John