√(20x^7y) * √(25x^13y^10) Multiplying radicals?
I need help with this problem, someone please explain in steps
√(20x^7y) * √(25x^13y^10) Index is 3
Update:index is the number that sits in the v of the radical sign. I cant figure out how to put the 3 in there.
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generally √a * √b = √ab
So we have
√ [(20x^7y)*(25x^13y^10)]
= √ [(20*25)*(x^7*x^13)*(y*y^10)]
= √ [(500)*(x^20)*(y^11)]
At this point you could simplify it further if you wish to get
√ [(5*100)*(x^20)*(y^11)]
= √100*√x^20*√y^10*√ [(5)*y)]
= 10*x^10*y^5*√(5*y)
What do you mean "index is 3"? Do you mean it's a "cube root" instead of a "square root"?
â(20x^7y) * â(25x^13y^10)
Combine under the radical sign...
â[(20x^7y)(25x^13y^10)]
â[(20*25)x^(7+13) y^(1+10)]
â[(500)x^(20) y^(11)]
If it's just a "square root"
â[(5*100)x^(20) y^(10)y]
â(100x^20y^10) * â(5y)
10x^(20/2)y^(10/2) * â(5y)
10x^10 y^5 * â(5y)
If it's a "cube root"
â[(500)x^(20) y^(11)]
â[(4*125)x^(18)x^2 y^(9)y^2]
â(125)x^(18)y^(9) * â[(4)x^2y^2]
5x^(18/3)y^(9/3) * â[(4)x^2y^2]
5x^(6)y^(3) * â[(4)x^2y^2]
â(20x^7y) * â(25x^13y^10)
= 10(x^10)(y^5)â(5y)
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Ideas: Take all square factors out of â.
Wow... now I remember why I hated math years ago...