Question

dau coroana si puncte ​

Answer 1

$\it a)\ \ \sqrt{16\cdot3^4}=\sqrt{16\cdot81}=4\cdot9=36\in\mathbb{Q}\\ \\ \\b)\ \ \sqrt[5]{\it3^{10}\cdot2^{-5}}=\sqrt[5]{\it(3^2)^5\cdot\dfrac{1}{2^5}}=\sqrt[5]{\it\dfrac{9^5}{2^5}}=\dfrac{9}{2}\in\mathbb{Q}\\ \\ \\ c)\ \ \sqrt[4]{\it81\cdot\dfrac{1}{256}}=\sqrt[4]{\it 3^4\cdot\dfrac{1}{4^4}}=\dfrac{3}{4}\in\mathbb{Q}$

$\it d)\ \ \sqrt[12]{\it8^2\cdot5^6}=\sqrt[12]{\it2^6\cdot5^6}=\sqrt[12]{\it 10^6}=10^{\frac{\ \ 6^{(2}}{12}}=10^{\frac{1}{2}}=\sqrt{10}\not\in\mathbb{Q}$