SOLUTION: Simplify. Assume all variables represent positive numbers. SQRT x^4y^3 Can anyone help me understand this type of problem. I am so lost with the concept pf trying to figure t

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Question 67869: Simplify. Assume all variables represent positive numbers.
SQRT x^4y^3
Can anyone help me understand this type of problem. I am so lost with the concept pf trying to figure this problem out. Thank you in advance as well!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
SQRT [x^4y^3 ]
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Separate the x^4y^3 into two factors;
Make the first factor be the highest possible perfect square factor
and let the 2nd factor be the remaining factor required.
In your problem:
Let the 1st factor be x^4y^2 because that is a perfect square.
Let the 2nd factor be y because that is the only piece missing.
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You now have sqrt[(x^4y^2)(y)]
Take the square root of the perfect square factor out of the radical
and leave the 2nd factor in the radical to get:
=x^2y sqrt(y)
That is the procdure to follow whenever you are simplifying square root.
For example:
sqrt(125) = sqrt(25*5)= 5sqrt5
sqrt(40) = sqrt(4*10) = 2sqrt10
sqrt(80) = sqrt(16*5)= 4sqrt5
Hope this helps.
Cheers,
Stan H.