How do you simplify #(2sqrt27)times(3 sqrt32)#?

3 Answers
Mar 24, 2017

Answer:

#72sqrt(6)#

Explanation:

#(color(blue)2sqrt(color(green)(27))) xx (color(red)3sqrt(color(magenta)(32)))#

#color(white)("XXX")=color(blue)2xxcolor(red)3xxsqrt(color(green)(3^3))xxsqrt(color(magenta)(2^5))#

#color(white)("XXX")=6 xx color(green)3sqrt(color(green)3)xxcolor(magenta)(2^2)sqrt(color(magenta)2)#

#color(white)("XXX")=6xxcolor(green)3xxcolor(magenta)(2^2)xxsqrt(color(green)3xxcolor(magenta)2)#

#color(white)("XXX")=72sqrt(6)#

Mar 24, 2017

Answer:

#72sqrt6#

Explanation:

Using the #color(blue)"law of radicals"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(sqrt(ab)hArrsqrtaxxsqrtb)color(white)(2/2)|)))#

To simplify the radicals consider the product of their factors of which one should be a #color(blue)"perfect square"#

#rArrsqrt27=sqrt(color(red)(9)xx3)=sqrtcolor(red)(9)xxsqrt3=3sqrt3#

#rArrsqrt32=sqrt(color(red)(16)xx2)=sqrtcolor(red)(16)xxsqrt2=4sqrt2#

#rArr2sqrt27xx3sqrt32#

#=2xx(3xxsqrt3)xx3xx(4xxsqrt2)#

#=(2xx3xx3xx4)xx(sqrt3xxsqrt2)#

#=72sqrt(3xx2)=72sqrt6#

Mar 24, 2017

Answer:

#72sqrt6#

Explanation:

#(2sqrt27) xx (3sqrt32)#

#:.=2sqrt(3*3*3) xx 3sqrt(2*2*2*2*2)#

#:.=2 xx 3sqrt3 xx 3*2*2sqrt2#

#:.=6sqrt3 xx 12sqrt2#

#:.=72sqrt3sqrt2#

#:.=72sqrt(2*3)#

#:.=72sqrt6#