Question

multiply and simplify.√6(√3+5√2)
please help

Answer 1

You can use the distributive property to multiply through by sqrt(6):
\[\sqrt6(\sqrt3+5\sqrt2)=\sqrt6*\sqrt3+\sqrt6*5\sqrt2)\]
Next you can aggregate under the roots:
\[\sqrt{6*3}+5\sqrt{6*2}=\sqrt{18}+5\sqrt{12}\]
Next factor out squares which divide 18 or 12 (9 divides 18 and 4 divides 12)
\[=\sqrt{9*2}+5\sqrt{4*3}=3\sqrt{2}+5*2\sqrt{3}=3\sqrt{2}+10\sqrt{3}\]