Question

Which of these four numbers
$\sqrt{{\pi }^2},\sqrt[3]{30.8},\sqrt[4]{4.00016},\sqrt[3]{3-1}.\sqrt{{\left(.09\right)}^{-1}}$ is (are) rational:

• A. none
• B. all
• C. the first and fourth
• D. only the fourth
• E. only the first

Answer 1

The correct option is D only the fourth

$\sqrt{{\pi }^2}=\pi$. irrational
$\sqrt[3]{38}=\sqrt[3]{3\frac{8}{10}}=\frac{2}{\sqrt[3]{310}}$, irrational
$\sqrt[4]{4.00016}=\sqrt[4]{416\times {10}^{-5}}=2.{10}^{-14}\sqrt[4]{4{10}^{-1}}$, irrational
$\sqrt[3]{3-1}.\sqrt{{\left(0.9\right)}^{-1}}=-1.\frac{1}{0.3}$= rational