How to simplify this?

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1 Answer
Somebody N.
Aug 31, 2017

#(6x^3y^3sqrt(15y))/sqrt(5xy)#

Explanation:

I am assuming the 3 before the radical in the numerator is not representing the 3rd root and the 12 is not a multiplier but a question number. If this is not the case then answer will be incorrect.

(1.) Factor the radicand in the numerator so you can extract roots.

#3sqrt(60x^6y^9)# can be factored as

# 3sqrt(4* 15 *x^6 *y^8 *y)#

(2.) Extract roots. It can be seen for example that the root of #x^6# is #x^3#, since #x^3 * x^3 => x^6# and root of #y^8# is #y^4# since #y^4 * y^4 => y^8#.

#6x^3y^4sqrt(15y)#

(3.) Do the same with the denominator.

#sqrt(5xy^3) => sqrt(5 * x * y^2 * y) => ysqrt(5xy)#

#(6x^3y^4sqrt(15y))/(ysqrt(5xy)#

(4.) Cancelling like factors gives:

#(6x^3y^3sqrt(15y))/sqrt(5xy)#

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