Question

Evaluate $(\sqrt{10}+\sqrt{11}+\sqrt{12})$$(\sqrt{10}+\sqrt{11}-\sqrt{12})$$(\sqrt{10}-\sqrt{11}+\sqrt{12})$$(\sqrt{10}-\sqrt{11}-\sqrt{12})$

• A. -440
• B. -359
• C. -358
• D. -521

Answer 1

Answer: (B)

-359

$\left[\right((\sqrt{10}+\sqrt{11})+\sqrt{12}\left)\right((\sqrt{10}+\sqrt{11})-\sqrt{12}\left)\right]\left[\right((\sqrt{10}-\sqrt{11})+\sqrt{12}\left)\right((\sqrt{10}-\sqrt{11})-\sqrt{12}\left)\right]$

$\Rightarrow \left[\right(\sqrt{10}+\sqrt{11}{)}^2-\left(\sqrt{12}{)}^2\right]\left[\right(\sqrt{10}-\sqrt{11}{)}^2-\left(\sqrt{12}{)}^2\right]$

$\Rightarrow (10+11+2\sqrt{10}\sqrt{11}-12)(10+11-2\sqrt{10}\sqrt{11}-12)$

$\Rightarrow (9+2\sqrt{110})(9-2\sqrt{110})$

$\Rightarrow \left(9{)}^2\right(2\sqrt{110}{)}^2$

$\Rightarrow 81-4\left(110\right)$

$\Rightarrow 81-440=-359$.