Step-by-step Solution

Multiply $\sqrt[3]{9}\cdot \sqrt[3]{\sqrt{2}+1}\cdot \sqrt[6]{27-2\cdot \sqrt{162}}$

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Step-by-step explanation

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.

$\sqrt[3]{9}\cdot \sqrt[3]{\frac{2}{\sqrt{2}}+1}\cdot \sqrt[6]{27-2\cdot \sqrt{162}}$

Unlock this full step-by-step solution!

Learn how to solve multiplication of numbers problems step by step online. Multiply 9^0.3333333333333333(2^0.5+1)^0.3333333333333333*(27-2162^0.5)^0.16666666666666666. 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. The square root of 162 is 9\sqrt{2}.

Final Answer

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

Time to solve it:

~ 0.02 s (SnapXam)