رادیکال

$\begin{array}{l}=\sqrt[5]{3^2}\\ \\ =\sqrt[5]{9}\end{array}$

$\begin{array}{l}=\sqrt[3]{{\left(-2\right)}^5}\\ \\ =\sqrt[3]{-32}\\ \\ =-\sqrt[3]{32}\end{array}$

$\begin{array}{l}=\sqrt[3]{7^{-2}}\\ \\ =\sqrt[3]{\frac{1}{49}}\end{array}$

$=\sqrt{5^3}$

$\begin{array}{l}=\sqrt[8]{{\left(-2\right)}^8}\\ \\ =-\left(-2\right)\\ \\ =2\end{array}$

$\begin{array}{l}=\sqrt[2k]{{\left(-5\right)}^{2k}}\\ \\ =-\left(-5\right)\\ \\ =5\end{array}$

$\begin{array}{l}={\left[\sqrt[6]{{\left(-4\right)}^6}\right]}^2\\ \\ =\sqrt[6]{{\left(-4\right)}^{6\times 2}}\\ \\ ={\left(-4\right)}^2\\ \\ =16\end{array}$

$\begin{array}{l}=\sqrt[3]{5^6}\\ \\ =\sqrt[3]{{\left(5^2\right)}^3}\\ \\ =5^2\\ \\ =25\end{array}$

$\begin{array}{l}={\left(\sqrt{2}\right)}^4\\ \\ =\sqrt{2^4}\\ \end{array}$

$\begin{array}{l}=\sqrt{{\left(2^2\right)}^2}\\ \\ =2^2\\ \\ =4\end{array}$

$\begin{array}{l}=\sqrt[5]{3^7}\\ \\ =\sqrt[5]{{\left(3\right)}^5\times {\left(3\right)}^2}\\ \\ =3\sqrt[5]{3^2}\\ \\ =3\sqrt[5]{9}\end{array}$

$\begin{array}{l}=\sqrt[3]{{\left(-3\right)}^2}\\ \\ =\sqrt[3]{9}\end{array}$

$\begin{array}{l}=\sqrt[3]{{\left(-4\right)}^5}\\ \\ =\sqrt[3]{-4^5}\\ \\ =-\sqrt[3]{4^5}\\ \end{array}$

$\begin{array}{l}=-\sqrt[3]{{\left(2^2\right)}^5}\\ \\ =-\sqrt[3]{2^{10}}\end{array}$

$\begin{array}{l}=-\sqrt[3]{2^9\times 2}\\ \\ =-\sqrt[3]{{\left(2^3\right)}^3\times 2}\\ \\ =-2^3\sqrt[3]{2}\\ \\ =-8\sqrt[3]{2}\end{array}$

$\begin{array}{l}=\sqrt[3]{{\left(-a^2\right)}^4}\\ \\ =\sqrt[3]{a^8}\\ \end{array}$

$\begin{array}{l}=\sqrt[3]{a^6\times a^2}\\ \\ =\sqrt[3]{{\left(a^2\right)}^3\times a^2}\\ \\ =a^2\sqrt[3]{a^2}\end{array}$

$\begin{array}{l}=\sqrt[5]{{\left(a^3{b}^2\right)}^3}\\ \\ =\sqrt[5]{a^9{b}^6}\\ \\ =\sqrt[5]{a^5{a}^4{b}^{5}b}\\ \\ =ab\sqrt[5]{a^{4}b}\end{array}$

$\begin{array}{l}={\left(\sqrt[7]{a^4}\right)}^6\\ \\ =\sqrt[7]{{\left(a^4\right)}^6}\\ \\ =\sqrt[7]{a^{24}}\\ \end{array}$

$\begin{array}{l}=\sqrt[7]{a^{21}{a}^3}\\ \\ =\sqrt[7]{{\left(a^3\right)}^7{a}^3}\\ \\ =a^3\sqrt[7]{a^3}\end{array}$

$\begin{array}{l}=\sqrt[3]{7^5}\times \sqrt[9]{7^3}\\ \\ =\sqrt[3]{7^5}\times \sqrt[3]{7}\\ \end{array}$

$\begin{array}{l}=\sqrt[3]{7^5\times 7}\\ \\ =\sqrt[3]{7^6}\\ \\ =7^2\\ =49\end{array}$

$\begin{array}{l}=\sqrt[3]{{\left(-2\right)}^2}\times \sqrt[6]{{\left(-2\right)}^2}\\ \\ =\sqrt[3]{2^2}\times \sqrt[3]{2}\\ \end{array}$

$\begin{array}{l}=\sqrt[3]{2^2\times 2}\\ \\ =\sqrt[3]{2^3}\\ \\ =2\end{array}$

$\begin{array}{l}=\sqrt[5]{{\left(-3\right)}^7}{\left(\sqrt[10]{3^2}\right)}^2\left(-\sqrt[5]{3}\right){\left(\sqrt[15]{3}\right)}^{30}\\ \\ =-\sqrt[5]{3^7}\times \sqrt[5]{3^2}\times \left(-\sqrt[5]{3}\right)\left(\sqrt[15]{3^{30}}\right)\\ \\ =\sqrt[5]{3^7\times 3^2\times 3}\times 3^2\\ \end{array}$

$\begin{array}{l}=\sqrt[5]{3^{10}}\times 3^2\\ \\ =3^2\times 3^2\\ \\ =3^4\\ \\ =81\end{array}$

$\begin{array}{l}\sqrt{{\left(0-1\right)}^2}\\ \\ =\sqrt{{\left(-1\right)}^2}\\ \\ =-\left(-1\right)\\ \\ =1\end{array}$

$\begin{array}{l}=\sqrt{{\left[{\left(-2\right)}^2-1\right]}^2}\\ \\ =\sqrt{{\left(4-1\right)}^2}\\ \\ =\sqrt{3^2}\\ \\ =3\end{array}$

$\begin{array}{l}=\sqrt{{\left(1^2-1\right)}^2}\\ \\ =\sqrt{{\left(1-1\right)}^2}\\ \\ =\sqrt{0^2}\\ \\ =0\end{array}$

$\begin{array}{l}=\sqrt{{\left[{\left(\sqrt{2}\right)}^2-1\right]}^2}\\ \\ =\sqrt{{\left(2-1\right)}^2}\\ \\ =\sqrt{1^2}\\ \\ =1\end{array}$

$\begin{array}{l}=\sqrt{{\left[{\left(-\sqrt{3}\right)}^2-1\right]}^2}\\ \\ =\sqrt{{\left(3-1\right)}^2}\\ \\ =\sqrt{2^2}\\ \\ =2\end{array}$

$\begin{array}{l}=\sqrt{{\left[{\left(4\right)}^2-1\right]}^2}\\ \\ =\sqrt{{\left(16-1\right)}^2}\\ \\ =\sqrt{{15}^2}\\ \\ =15\end{array}$

$\begin{array}{l}=\sqrt{{\left[{\left(0.1\right)}^2-1\right]}^2}\\ \\ =\sqrt{{\left(0.01-1\right)}^2}\\ \end{array}$

$\begin{array}{l}=\sqrt{{\left(-0.99\right)}^2}\\ \\ =-\left(-0.99\right)\\ \\ =0.99\end{array}$