Question

The simplified value of $(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})(\sqrt{8}-2)(\sqrt{12}+\sqrt{8})$ is

• A. 3
• B. 4
• C. 2
• D. 1

Answer 1

The correct option is B 4

$(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})(\sqrt{8}-2)(\sqrt{12}-\sqrt{8})$

=$(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})\left[2(\sqrt{2}-1)\right]\left[2(\sqrt{3}-\sqrt{2})\right]$

=$4(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})(\sqrt{2}-1)(\sqrt{3}-\sqrt{2})$

=$4(2-1)(3-2)=4$