Question

Multiply and simplify:

Answer 1

Consider this:

Answer 2

do you understand or do you still want some help?

Answer 3

SO WHAT DID YOU DO WHEN YOU GOT THE 4?

Answer 4

First distribute the radical six to the other numbers in radicals:\[\sqrt6(\sqrt3+5\sqrt2)=\sqrt{6*3}+5\sqrt{2*6}=\sqrt{18}+5\sqrt{12}\]We then try to factor what is in the radical into a perfect square times some number:\[\sqrt{18}+5\sqrt{12}=\sqrt{9*2}+5\sqrt{4*3}\]then note that \[\sqrt9=3\]and\[\sqrt4=2\]so we can simplify the above by pulling out the perfect squares from the radical sign:
\[=\sqrt{9*2}+5\sqrt{3*4}=3\sqrt2+(5*2)\sqrt3=3\sqrt2+10\sqrt3\]More clear?