Sure! Let's break down the problem step by step to find the value of [tex]\(\sqrt[4]{\sqrt[3]{2^2}}\)[/tex].
1. First, calculate [tex]\(2^2\)[/tex]:
- [tex]\[ 2^2 = 4 \][/tex]
2. Next, find the cube root of the result from step 1:
- [tex]\[ \sqrt[3]{4} \approx 1.5874010519681994 \][/tex]
3. Finally, find the fourth root of the result from step 2:
- [tex]\[ \sqrt[4]{1.5874010519681994} \approx 1.122462048309373 \][/tex]
So, putting everything together, we have:
[tex]\[ \sqrt[4]{\sqrt[3]{2^2}} = 1.122462048309373 \][/tex]
The closest option to this number is not listed among the provided choices (a), (c), or (d).
Therefore, the value of [tex]\(\sqrt[4]{\sqrt[3]{2^2}}\)[/tex] is approximately:
[tex]\[ 1.122462048309373 \][/tex]
