指出下列哪些数是无理数。 $0.5, \; \frac{\pi}{2}, \; 2\sqrt{2}, \; 3\sqrt{3}\times\sqrt{3}$ 答案 ...

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完整解法

1. Identify which given numbers cannot be written as rational numbers

$0.5=\dfrac{1}{2}$ , so it is rational.

$\dfrac{\pi}{2}$ is irrational since $\pi$ is irrational.

$2\sqrt{2}$ is irrational since $\sqrt{2}$ is irrational.

$3\sqrt{3}\times\sqrt{3}=3\times 3=9$ , so it is rational.

Therefore, the irrational numbers are $\dfrac{\pi}{2}$ and $2\sqrt{2}$ .

答案

$\dfrac{\pi}{2},\; 2\sqrt{2}$

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