Question

\(\sqrt{\left(\sqrt{2}-3\right)^2}.\sqrt{11+6\sqrt{2}}\)

Answer 1

\(\sqrt{\left(\sqrt{2}-3\right)^2}.\sqrt{11+6\sqrt{2}}=|3-\sqrt{2}|.\sqrt{9+2.3\sqrt{2}+2}=\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)=9-2=7\)

Answer 2

\(\sqrt{\left(\sqrt{2}-3\right)^2}.\sqrt{11+6\sqrt{2}}\)

\(=\left|\sqrt{2}-3\right|.\sqrt{\left[3^2+2.3.\sqrt{2}+\left(\sqrt{2}\right)^2\right]}\)

\(=-\left(\sqrt{2}-3\right).\sqrt{\left(3+\sqrt{2}\right)^2}\)

\(=\left(3-\sqrt{2}\right).\left(3+\sqrt{2}\right)\)

\(=9^2-\left(\sqrt{2}\right)^2=9-2=7\)

Answer 3

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