Question

$[\frac{3}{\sqrt{19-2\sqrt{88}}}-\frac{8}{\sqrt{14+2\sqrt{33}}}].(\sqrt{8}-\sqrt{3})=$

• A. $\sqrt{5}$
• B. $\sqrt{8}$
• C. $-3$
• D. $5$

Answer 1

The correct option is D $5$

$\sqrt{19-2\sqrt{88}}=\sqrt{{(\sqrt{11}-\sqrt{8})}^2}=\sqrt{11}-\sqrt{8}$

$\sqrt{14+2\sqrt{33}}=\sqrt{{(\sqrt{11}+\sqrt{3})}^2}=\sqrt{11}+\sqrt{3}$

$(\frac{3}{\sqrt{19-2\sqrt{88}}}-\frac{8}{\sqrt{14+2\sqrt{33}}})(\sqrt{8}-\sqrt{3})=(\frac{3}{\sqrt{11}-\sqrt{8}}-\frac{8}{\sqrt{11}+\sqrt{3}})(\sqrt{8}-\sqrt{3})=(\sqrt{11}+\sqrt{8}-\sqrt{11}+\sqrt{3})(\sqrt{8}-\sqrt{3})=5$

Therefore correct option is $D$