what is the following product?\n$(sqrt{14}-sqrt{3})(sqrt{12}+sqrt{7})$ \n$2sqrt{42}+7sqrt{2}-6…

what is the following product?\n$(sqrt{14}-sqrt{3})(sqrt{12}+sqrt{7})$ \n$2sqrt{42}+7sqrt{2}-6 - sqrt{21}$\n$sqrt{14}-6+sqrt{7}$\n$sqrt{26}+sqrt{21}-sqrt{15}-sqrt{10}$\n$2sqrt{42}-sqrt{21}$

what is the following product?\n$(sqrt{14}-sqrt{3})(sqrt{12}+sqrt{7})$ \n$2sqrt{42}+7sqrt{2}-6 - sqrt{21}$\n$sqrt{14}-6+sqrt{7}$\n$sqrt{26}+sqrt{21}-sqrt{15}-sqrt{10}$\n$2sqrt{42}-sqrt{21}$

Answer

Explanation:

Step1: Use FOIL method

$(\sqrt{14}-\sqrt{3})(\sqrt{12}+\sqrt{7})=\sqrt{14}\times\sqrt{12}+\sqrt{14}\times\sqrt{7}-\sqrt{3}\times\sqrt{12}-\sqrt{3}\times\sqrt{7}$

Step2: Simplify square - root products

$\sqrt{14}\times\sqrt{12}=\sqrt{14\times12}=\sqrt{168}=\sqrt{4\times42}=2\sqrt{42}$; $\sqrt{14}\times\sqrt{7}=\sqrt{14\times7}=\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}$; $\sqrt{3}\times\sqrt{12}=\sqrt{3\times12}=\sqrt{36}=6$; $\sqrt{3}\times\sqrt{7}=\sqrt{21}$

Step3: Combine results

$2\sqrt{42}+7\sqrt{2}-6 - \sqrt{21}$

Answer:

$2\sqrt{42}+7\sqrt{2}-6 - \sqrt{21}$