Question

Use a propriedade do produto das raizes e determine o valor :

  √4.25
  √$\sqrt[4]{3} ^{12}$
  √49.9.4.1
  √4. √25.100

Answer 1

$a) \sqrt{4\cdot25}=\sqrt{4}\cdot\sqrt{25}= 2\cdot5= 10\\ \\ b) \sqrt{ \sqrt[4]{3^{12}}} =\sqrt[2\cdot4]{3^{12}} =\sqrt[8]{3^{12}} =\sqrt[8:4]{3^{12:4}} =\sqrt[]{3^{3}} = \sqrt{3^2\cdot3} \\ =\sqrt{3^2}\cdot\sqrt{3} =3\sqrt{3}\\ \\ c) \sqrt{49\cdot9\cdot4\cdot1} =\sqrt{49}\cdot\sqrt{9}\cdot\sqrt{4}\cdot\sqrt{1} =7\cdot3\cdot2\cdot1 =42\\ \\ d) \sqrt{4}\cdot\sqrt{9\cdot100} =\sqrt{4}\cdot\sqrt{9}\cdot\sqrt{100} =2\cdot3\cdot10 =60$