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

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Answer 1 · 2018-04-23T19:30:22

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

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

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

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

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

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

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

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

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

How do I add radicals with different bases sqrt150 +sqrt40sqrt150 +sqrt40?