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. Check which given numbers are rational or simplify to rational numbers

$0.5=\dfrac12$ , so $0.5$ is rational.

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

2. Identify the irrational numbers

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

$2\sqrt{2}$ is irrational since $\sqrt{2}$ is irrational and multiplying by $2$ does not make it rational.

答案

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

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