Задание
ТЕОРИЯ
Свойства арифметического корня
| \(\displaystyle 1)\) | \(\displaystyle \sqrt[n\,]{ab}=\sqrt[n]{a} \cdot \sqrt[n]{b}{\small}\) при \(\displaystyle a \geqslant 0 {\small,}\)\(\displaystyle b \geqslant 0{\small,}\)\(\displaystyle n \in \N{\small,}\) |
| \(\displaystyle 2)\) | \(\displaystyle \sqrt[n\,]{\frac{a}{b}}={\frac{\sqrt[n]{a}}{\sqrt[n]{b}}}{\small}\) при \(\displaystyle a \geqslant 0 {\small,}\)\(\displaystyle b > 0{\small,}\)\(\displaystyle n \in \N{\small,}\) |
| \(\displaystyle 3)\) | \(\displaystyle \sqrt[n\,]{\sqrt[m\,]{a}} =\sqrt[nm\,]{a}\) при \(\displaystyle a \geqslant 0 {\small,}\)\(\displaystyle n \in \N{\small,}\)\(\displaystyle m \in \N{\small,}\) |
| \(\displaystyle 4)\) | \(\displaystyle \left(\sqrt[n\,]{a}\right)^{\!m}=\sqrt[n]{a^m} \)при \(\displaystyle a > 0 {\small,}\)\(\displaystyle n \in \N{\small,}\)\(\displaystyle m\)– целое, |
| \(\displaystyle 5)\) | \(\displaystyle \sqrt[nk\,]{ a^{mk}}=\sqrt[n\,]{ a^{m}}\) при \(\displaystyle a \geqslant 0 {\small,}\)\(\displaystyle n \in \N{\small,}\)\(\displaystyle k \in \N{\small,}\)\(\displaystyle m \in \N{\small.}\) |
Решение