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## Step-by-step Solution

Problem to solve:

$9^{\frac{1}{3}}\left(\sqrt{2}+1\right)^{\frac{1}{3}}\left(27-2\sqrt{162}\right)^{\frac{1}{6}}$

Learn how to solve multiplication of numbers problems step by step online.

$\sqrt[3]{9}\cdot \left(\sqrt{2}+1\right)^{\frac{1}{3}}\cdot \left(27-2\cdot \sqrt{162}\right)^{\frac{1}{6}}$

Learn how to solve multiplication of numbers problems step by step online. Multiply 9^(1/3)(2^0.5+1)^(1/3)*(27-2162^0.5)^(1/6). Divide 1 by 3. The square root of 2 is \frac{2}{\sqrt{2}}. Calculate the power \sqrt[3]{9}. Add the values \frac{2}{\sqrt{2}} and 1.

$3$
$9^{\frac{1}{3}}\left(\sqrt{2}+1\right)^{\frac{1}{3}}\left(27-2\sqrt{162}\right)^{\frac{1}{6}}$