How do you simplify #sqrt((3x^3)/(64x^2))#?

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Answer 1 · 2017-04-05T15:39:12

#sqrt(3x)/8#

Remember that if you dividing under a root, you can split it into two separate roots:

#sqrt((3x^3)/(64x^2)) = (sqrt(3x^3))/(sqrt(64x^2)) = (sqrt(3x xx x^2))/(sqrt(64x^2)#

Now find the square roots where you can:

#(sqrt(3x xx color(red)(x^2)))/(sqrt(color(blue)(64x^2)))=(color(red)(x)sqrt(3x))/(color(blue)(8x))#

Now simplify:

#sqrt(3x)/8#

OR you could simplify under the root first:

#sqrt((3x^3)/(64x^2)) = sqrt((3x)/(64))#

#= sqrt(3x)/8#