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1. \((\sqrt{a})^2 = a\) , если \(a\ge0\) ;
2. \(\sqrt{a\cdot b}=\sqrt{a}\cdot \sqrt{b}\) , если \(a\ge0\) и \(b\ge0\) .
3. \(\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\) , если \(a\ge0\) и \(b\gt0\) .
4. \(\sqrt{a^{2n}}=\lvert{a^n}\rvert\)

Пример:

1. \(\sqrt{3}\cdot \sqrt{12}=\sqrt{3\cdot 12}=\sqrt{36}=\) [ ];
2. \(\sqrt{225\cdot 4}=\sqrt{225}\cdot \sqrt{4}=\) [ ];
3. \(\sqrt{\dfrac{16}{25}}=\dfrac{\sqrt{16}}{\sqrt{25}}=\) [ ];
4. \(\sqrt{5^6}=5^3=\) [ ];
5. \(\sqrt{(-5)^6}=\lvert{(-5)^3}\rvert=\) [ ].