Question

Gente PF... Ajudem emploro

Answer 1

$3)\ Para\ \sqrt{5} = 2,24\\\\ a) \sqrt{125} = \sqrt{5 \times 5\times 5}=5\sqrt{5} =11,2\\\\ b)\ \sqrt{20} = \sqrt{2 \times 2 \times 5} = 2\sqrt{5} = 4,48\\\\ c)\ \sqrt{500} = \sqrt{2 \times 2 \times 5 \times 5 \times 5}=2\times5\sqrt{5}=10\sqrt{5}=22,4\\\\ d)\ \sqrt{\frac{1}{5}}=\dfrac{\sqrt{1}}{\sqrt{5}}=\dfrac{1}{2,24}\\\\ e)\ \sqrt{605} = \sqrt{11 \times 11 \times 5}=11\sqrt{5} = 24,64$

$f)\ \sqrt{\frac{45}{4}}=\dfrac{\sqrt{45}}{\sqrt{4}}=\dfrac{\sqrt{3 \times 3 \times 5}}{\sqrt{2 \times 2}}=\dfrac{3\sqrt{5}}{2}=\dfrac{6,72}{2}=3,36\\\\ g)\ \sqrt{\frac{80}{81}}=\dfrac{\sqrt{80}}{\sqrt{81}}=\dfrac{\sqrt{2 \times2 \times 2 \times 2 \times 5}}{\sqrt{3 \times 3 \times 3 \times 3}}=\dfrac{2\times2\sqrt{5}}{3 \times 3}=\dfrac{4\sqrt{5}}{9}=\dfrac{8,96}{9}$

$h)\ \sqrt{\frac{720}{441}}=\dfrac{\sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5}}{\sqrt{3 \times 3 \times 7 \times 7}}=\dfrac{2 \times 2 \times 3\sqrt{5}}{3 \times 7}=\dfrac{12\sqrt{5}}{21}\\\\ \Rightarrow \dfrac{26,88}{21}$



$4)\\\\ a)\ \sqrt{4}-\sqrt[4]{1}=\sqrt{2 \times 2}-\sqrt[4]{1}=2-1=1\\\\ b)\ -\sqrt[1]{-1}+\sqrt{121}=-(-1)+\sqrt{11 \times 11}=1+11=12\\\\ c)\ 5\sqrt[3]{8}-\frac{7}{2}\sqrt{25}=5\times\sqrt[3]{2\times 2 \times 2}-\frac{7}{2}\sqrt{5 \times 5}=5\times2 - \dfrac{7 \times 5}{2}\\\\ \Rightarrow 10-\dfrac{35}{2}=\dfrac{-35+20}{2}=-\dfrac{15}{2}$

$d)\ \dfrac{2\sqrt{4} + \sqrt[4]{16}}{2\sqrt[3]{27}}=\dfrac{2\sqrt{2 \times 2} + \sqrt[4]{2 \times 2 \times 2 \times 2}}{2\sqrt[3]{3 \times 3 \times 3}}=\dfrac{2 \times 2 + 2 \times 2}{2 \times 3}\\\\ \Rightarrow \dfrac{4 + 4}{6}=\dfrac{8}{6}=\dfrac{4}{3}$



$5)\\\\ a)\ \sqrt{x}\ \ \Rightarrow\ \ x \ \geq 0\\\\ b)\ \sqrt[3]{-x}\ \ \Rightarrow \ \ x = \mathbb{R}\\\\ c)\ \sqrt[4]{\frac{1}{x}}=\dfrac{\sqrt[4]{1}}{\sqrt[4]{x}}=\dfrac{1}{\sqrt[4]{x}}\ \ \Rightarrow \ \ x\ \textgreater \ 0$



$6)\\\\ a)\ (2\sqrt{7}) \times (3\sqrt{5})=2\times 3 \sqrt{7 \times 5}=6\sqrt{35}\\\\ b)\ (3 \sqrt[3]{2}) \times (5 \sqrt[3]{6}) \times (8 \sqrt[3]{4})=3 \times 5 \times 8 \sqrt[3]{2 \times 6 \times 4}=120\sqrt[3]{48}\\\\ \Rightarrow 120\sqrt[3]{2 \times 2 \times 2 \times 2 \times 3}=120 \times 2 \sqrt[3]{2 \times 3}=240\sqrt[3]{6}\\\\ c)\ \dfrac{(10\sqrt{6})}{(5\sqrt{2})}=\dfrac{10}{5} \times \dfrac{\sqrt{6}}{\sqrt{2}}=2 \times \sqrt{\frac{6}{2}}=2\sqrt{3}$

$d)\ \dfrac{(6\sqrt[4]{30})}{(3\sqrt[4]{5})}=\dfrac{6}{3} \times \dfrac{\sqrt[4]{30}}{\sqrt[4]{5}}=2 \times \sqrt[4]{\frac{30}{5}}=2\sqrt[4]{6}$



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