#(4 sqrt 3xy^3) (-2 sqrt 6x^3y^2)? #Multiply the radical expression

1 Answer
Oct 31, 2017

Answer:

#-24sqrt(2)x^4y^5#

Explanation:

#(4sqrt(3)xy^3)(-2sqrt(6)x^3y^2)#

decomposing each factor:
#color(white)("XXX")=(4xxsqrt(3)xx x xx y^3)xx((-2) xx sqrt(6) xx x^3 xx y^2)#

regrouping like factors:
#color(white)("XXX")=(4 xx(-2))xx(sqrt(3)xxsqrt(6))xx(x xx x^3)xx(y^3 xxy^2)#

combining like factors:
#color(white)("XXX")=(-8) xx (sqrt(18)) xx (x^4) xx (y^5)#

simplifying the #sqrt(18)# factor
#color(white)("XXX")=(-8) xx (3sqrt(2)) xx (x^4) xx (y^5)#

combining the two constant factors
#color(white)("XXX")=(-24sqrt(2)) xx (x^4) xx (y^5)#

back into (compressed) standard form:
#color(white)("XXX")=-24sqrt(2)x^4y^5#