Question

How do I convert 8.485281374 into a radical?

Answer 1

Recall that something inside a radical, comes out only if it's raised to the same root as the radical, for examples,

$\bf \sqrt{25}\implies \sqrt{5^2}\implies \sqrt[2]{5^2}\implies 5 \\\\\\ \sqrt{27}\implies \sqrt{3^3}\implies \sqrt[3]{3^3}\implies 3 \\\\\\ \textit{one can also say that}\qquad 5=\sqrt[2]{5^2}~~or~~3=\sqrt[3]{3^3}\\\\ -------------------------------$

$\bf therefore\qquad 8.485281374= \begin{cases} \sqrt[2]{8.485281374^2}\\\\ \sqrt[3]{8.485281374^3}\\\\ \sqrt[7]{8.485281374^7}\\\\ \sqrt[11]{8.485281374^{11}}\\\\ \sqrt[x]{8.485281374^x} \end{cases}\impliedby \textit{any is valid} \\\\\\ \textit{so say then}\qquad 8.485281374=\sqrt[2]{8.485281374^2} \\\\\\ 8.485281374=\sqrt{71.999999995951327876}$