abstract algebra - Degree of a finite field extension. How to find?

What is the degree of the extension $[\mathbb Q(\sqrt2 + \sqrt3 + \sqrt5) : \mathbb Q ]$?

Can you explain, what I must to do in this example?

Answer

$[\mathbb Q(\sqrt2 + \sqrt3 + \sqrt5) : \mathbb Q ]=[\mathbb Q(\sqrt2 , \sqrt3 , \sqrt5) : \mathbb Q ]=[\mathbb Q(\sqrt2 ,\sqrt3 , \sqrt5) : \mathbb Q (\sqrt2 , \sqrt3)].[\mathbb Q(\sqrt2 ,\sqrt3 ) : \mathbb Q (\sqrt2 )].[\mathbb Q(\sqrt2 ) : \mathbb Q ]=2.2.2=8$

$\mathbb Q(\sqrt2 + \sqrt3 + \sqrt5) $ is a $8 $ degree extension over $Q$.And basis are $1,\sqrt2,\sqrt3,\sqrt5,\sqrt6,\sqrt{10},\sqrt{15},\sqrt{30}$