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\sqrt[3]{\left(\sqrt{5}\right)^{2}-4}
Consider \left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.
\sqrt[3]{5-4}
The square of \sqrt{5} is 5.
\sqrt[3]{1}
Subtract 4 from 5 to get 1.
1
Calculate \sqrt[3]{1} and get 1.