How do you simplify #-3sqrt2+3sqrt20-3sqrt8#?

1 Answer
Apr 10, 2017

Answer:

#6sqrt5-9sqrt2#

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)|)))#

#rArrsqrt20=sqrt(4xx5)=sqrt4xxsqrt5=2sqrt5#

#"and " sqrt8=sqrt(4xx2)=sqrt4xxsqrt2=2sqrt2#

#rArr-3sqrt2+3sqrt20-3sqrt8#

#=-3sqrt2+3(2sqrt5)-3(2sqrt2)#

#=-3sqrt2+6sqrt5-6sqrt2#

#=6sqrt5-9sqrt2larrcolor(red)" collect like terms"#