Real numbers : $a,b,c$

Natural number : $n,m$

• ${\sqrt[n]{a}}=a^{\dfrac{1}{n}}$
• $\sqrt[n]{ab}=\sqrt[n]{a} \times \sqrt[n]{b}$
• $\sqrt[n]{\dfrac{a}{b}} =\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$
• ${(\sqrt[n]{a})}^n=a$
• $\sqrt[m]{\sqrt[n]{a}} =\sqrt[mn]{a}$
• ${(\sqrt[n]{a})^m} =\sqrt[n]{a^m}$
• $\sqrt{a\cdot \sqrt{a\cdot\sqrt{a\cdot\sqrt{a\cdot\cdot \cdot n\ \text{times}}}}}$ $= a^{1-\dfrac{1}{2^n}}$
• $\sqrt{a\cdot \sqrt{a\cdot\sqrt{a\cdot\sqrt{a\cdot\cdot \cdot \infty}}}} = a$