Question 31

simplify $$(\sqrt {8}+3)+(\frac {1}{3-\sqrt{8}})-(6+4\sqrt {2})$$

Solution

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$$\frac{1}{\left(3-\sqrt{8\ }\right)}=\frac{\left(3+\sqrt{8\ }\right)}{9-8}=\left(3+\sqrt{8\ }\right).$$

So, $$(\sqrt{8}+3)+(\frac{1}{3-\sqrt{8}})-(6+4\sqrt{2}).$$

$$\left(=(\sqrt{8}+3)+(3+\sqrt{8\ }\right)-(6+4\sqrt{2}).$$

$$=\left(6+2\sqrt{8\ }\right)-(6+4\sqrt{2}).$$

$$=\left(6+4\sqrt{2}\right)-(6+4\sqrt{2}).$$

$$=0.$$

C is correct choice.

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