Question

(2radical7 + radical 11) (radical7-3 radical 11)

multiply and simplify. assume all variables represent nonnegative numbers

Answer 1

\[\frac{2\sqrt{7}+\sqrt{11}}{\sqrt{7}-3\sqrt{11}}\]?

Answer 2

if so multiply top and bottom by "conjugate" of denominator, namely
\[\sqrt{7}+3\sqrt{11}\]

Answer 3

because
\[(\sqrt{7}-3\sqrt{11})(\sqrt{7}+3\sqrt{11})=7-9\times 11=7-99=-92\]

Answer 4

you get


\[\frac{2\sqrt{7}+\sqrt{11}}{\sqrt{7}-3\sqrt{11}}\times \frac{\sqrt{7}+3\sqrt{11}}{\sqrt{7}+3\sqrt{11}}\]?

Answer 5

\[=\frac{14+7\sqrt{77}+33}{-92}\]
\[=\frac{47+7\sqrt{7}}{-92}\]

Answer 6

nope not right.