Question

simplify.

• \\(sqrt4{80} + 4sqrt4{405}\\)

Explanation:

Step1: Simplify $\sqrt[4]{80}$

Factor 80: $80 = 16\times5 = 2^4\times5$. So, $\sqrt[4]{80}=\sqrt[4]{2^4\times5}=2\sqrt[4]{5}$. Then $-\sqrt[4]{80}=-2\sqrt[4]{5}$.

Step2: Simplify $4\sqrt[4]{405}$

Factor 405: $405 = 81\times5 = 3^4\times5$. So, $\sqrt[4]{405}=\sqrt[4]{3^4\times5}=3\sqrt[4]{5}$. Then $4\sqrt[4]{405}=4\times3\sqrt[4]{5}=12\sqrt[4]{5}$.

Step3: Combine the terms

Now, substitute the simplified forms back into the original expression: $-\sqrt[4]{80}+4\sqrt[4]{405}=-2\sqrt[4]{5}+12\sqrt[4]{5}$. Combine like terms: $(-2 + 12)\sqrt[4]{5}=10\sqrt[4]{5}$.

Answer:

$10\sqrt[4]{5}$