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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].
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].
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