Prove the inequality.Let a, b and c be nonnegative real numbers. Let $a$, $b$ and $c$ be nonnegative real numbers. Prove that $a^4+b^4+c^2\ge 8^{½}abc$

Using AM,GM Inequality 
$$a^4+b^4\ge 2a^2b^2$$ which can be demonstrated as  $$a^4+b^4=(a^2-b^2)^2+2a^2b^2\ge 2a^2b^2$$ as the square of any real number is $\displaystyle\not<0$
Again similarly, $$2a^2b^2+c^2\ge 2\sqrt{2a^2b^2\cdot c^2}$$
