How do I add radicals with different bases #sqrt150 +sqrt40#?

1 Answer
Apr 23, 2018

Answer:

#sqrt(150)+sqrt(40)=sqrt(2)(5sqrt(3)+2sqrt(5))=sqrt(10(19+4sqrt(15)))#

Explanation:

Hmm. Not sure if this is what you want, but you could write this as a single, NESTED radical.

#sqrt(150)+sqrt(40)=sqrt(5^2(3)(2))+sqrt(2^2(5)(2))#

#=5sqrt(3)sqrt(2)+2sqrt(5)sqrt(2)#

#=sqrt(2)(5sqrt(3)+2sqrt(5))#

#=sqrt(2)sqrt((5sqrt(3)+2sqrt(5))^2)#

#=sqrt(2)sqrt(95+20sqrt(15))#

#=sqrt(2)sqrt(5(19+4sqrt(15)))#

#=sqrt(10(19+4sqrt(15)))#