what is the following product?\n$(sqrt{12}+sqrt{6})(sqrt{6}-sqrt{10})$ \n$6sqrt{2}-2sqrt{30}+6…

what is the following product?\n$(sqrt{12}+sqrt{6})(sqrt{6}-sqrt{10})$ \n$6sqrt{2}-2sqrt{30}+6 - 2sqrt{15}$\n$6sqrt{3}-6sqrt{5}$\n$3sqrt{2}-sqrt{22}+2sqrt{3}-4$\n$2sqrt{3}+6 - 2sqrt{15}$
Answer
Explanation:
Step1: Use FOIL method
$(\sqrt{12}+\sqrt{6})(\sqrt{6}-\sqrt{10})=\sqrt{12}\times\sqrt{6}-\sqrt{12}\times\sqrt{10}+\sqrt{6}\times\sqrt{6}-\sqrt{6}\times\sqrt{10}$
Step2: Simplify square - root multiplications
$\sqrt{12}\times\sqrt{6}=\sqrt{12\times6}=\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}$; $\sqrt{12}\times\sqrt{10}=\sqrt{12\times10}=\sqrt{120}=\sqrt{4\times30}=2\sqrt{30}$; $\sqrt{6}\times\sqrt{6}=6$; $\sqrt{6}\times\sqrt{10}=\sqrt{6\times10}=\sqrt{60}=\sqrt{4\times15}=2\sqrt{15}$.
Step3: Combine results
$6\sqrt{2}-2\sqrt{30}+6 - 2\sqrt{15}$
Answer:
$6\sqrt{2}-2\sqrt{30}+6 - 2\sqrt{15}$