Final answer to the problem
$\sqrt[3]{9\sqrt{2}+9}\sqrt[6]{27-18\sqrt{2}}$
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Step-by-step Solution
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- Write in simplest form
- Prime Factor Decomposition
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
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1
Apply the property of power of a product in reverse: $a^n\cdot b^n=(a\cdot b)^n$
$\sqrt[3]{9\left(\sqrt{2}+1\right)}\sqrt[6]{27-2\sqrt{162}}$
Learn how to solve product of radicals problems step by step online.
$\sqrt[3]{9\left(\sqrt{2}+1\right)}\sqrt[6]{27-2\sqrt{162}}$
Learn how to solve product of radicals problems step by step online. Simplify the product of radicals 9^(1/3)(2^(1/2)+1)^(1/3)(27-2162^(1/2))^(1/6). Apply the property of power of a product in reverse: a^n\cdot b^n=(a\cdot b)^n. Multiply the single term 9 by each term of the polynomial \left(\sqrt{2}+1\right). Rewrite 162 as a power. The power of a product is equal to the product of it's factors raised to the same power.
Final answer to the problem
$\sqrt[3]{9\sqrt{2}+9}\sqrt[6]{27-18\sqrt{2}}$
Exact Numeric Answer
$3$
