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Simplify:

(i) [tex]\sqrt[4]{\sqrt[3]{2^2}}[/tex]


Sagot :

To simplify the expression [tex]\(\sqrt[4]{\sqrt[3]{2^2}}\)[/tex], we should work through it step-by-step, starting from the inside and working our way out. Let's break it down:

1. Evaluate the innermost expression [tex]\(2^2\)[/tex]
[tex]\[ 2^2 = 4 \][/tex]
So, the expression now becomes:
[tex]\[ \sqrt[4]{\sqrt[3]{4}} \][/tex]

2. Calculate the cube root of 4
[tex]\[ \sqrt[3]{4} \approx 1.5874010519681994 \][/tex]

Therefore, the expression now is:
[tex]\[ \sqrt[4]{1.5874010519681994} \][/tex]

3. Finally, calculate the fourth root of [tex]\(1.5874010519681994\)[/tex]
[tex]\[ \sqrt[4]{1.5874010519681994} \approx 1.122462048309373 \][/tex]

So, after simplifying the given expression [tex]\(\sqrt[4]{\sqrt[3]{2^2}}\)[/tex], the final result is approximately [tex]\(1.122462048309373\)[/tex].