Question

Simplify 3/ whole root 19-2 root 88 - 8/ whole root 14 + 2 root 33

Answer 1

Dear student
$$\begin{gathered} \frac{3}{\sqrt{19-2\sqrt{88}}}-\frac{8}{\sqrt{14+2\sqrt{33}}} \\ =\frac{3}{\sqrt{19-4\sqrt{22}}}-\frac{8}{\sqrt{14+2\sqrt{33}}} \\ =\frac{3\left(\sqrt{19-4\sqrt{22}}\right)}{19-4\sqrt{22}}-\frac{8\sqrt{14+2\sqrt{33}}}{14+2\sqrt{33}} \\ =\frac{3\left(\sqrt{19-4\sqrt{22}}\right)}{19-4\sqrt{22}}\times \frac{19+4\sqrt{22}}{19+4\sqrt{22}}-\frac{8\sqrt{14+2\sqrt{33}}}{14+2\sqrt{33}}\times \frac{14-2\sqrt{33}}{14-2\sqrt{33}} \\ =\frac{3\left(\sqrt{19-4\sqrt{22}}\right)\left(19+4\sqrt{22}\right)}{9}-\frac{8\left(\sqrt{14+2\sqrt{33}}\right)\left(14-2\sqrt{33}\right)}{64} \end{gathered}$$
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