Question

# To simplify: The given redical: An expression: displaystyle{sqrt[{{4}}]{{{left({x}^{2}-{4}right)}^{4}}}}. Use absolute value bars when necessary.

To simplify:
The given redical:
An expression: $$\displaystyle{\sqrt[{{4}}]{{{\left({x}^{2}-{4}\right)}^{4}}}}.$$
Use absolute value bars when necessary.

2020-11-09
Calculation:
$$\displaystyle{\sqrt[{{4}}]{{{\left({x}^{2}-{4}\right)}^{4}}}}$$
$$\displaystyle\Rightarrow{\left({x}^{2}-{4}\right)}^{{\frac{4}{{4}}}}\ \text{(Applying rule} \displaystyle{\sqrt[{{n}}]{{{a}^{m}}}}={a}^{{\frac{m}{{n}}}})$$
$$\displaystyle\Rightarrow{\left({x}^{2}-{4}\right)}^{1}$$
$$\displaystyle\Rightarrow{x}^{2}-{4}$$
So, we need to take absolute value of $$x^{2}\ -\ 4,$$ to make the solution thue for all values of x.
Therefore, the simplified form of the given expression would be $$\displaystyle{\left|{x}^{2}-{4}\right|}.$$