化简 $: \frac{\sqrt{0.2209}+\sqrt{0.1681}}{\sqrt{0.2209}-\sqrt{0.1681}}$

待办事项

我们需要化简 $: \frac{\sqrt{0.2209}+\sqrt{0.1681}}{\sqrt{0.2209}-\sqrt{0.1681}}$.

解答

$=\frac{\sqrt{0.2209}+\sqrt{0.1681}}{\sqrt{0.2209}-\sqrt{0.1681}}$

为了分解分母，我们乘以并除以 $\sqrt{0.2209}-\sqrt{0.1681}$。

因此，

$\begin{array}{l} \frac{\sqrt{0.2209} +\sqrt{0.1681}}{\sqrt{0.2209} -\sqrt{0.1681}} =\frac{\left(\sqrt{0.2209} +\sqrt{0.1681}\right)\left(\sqrt{0.2209} +\sqrt{0.1681}\right)}{\left(\sqrt{0.2209} -\sqrt{0.1681}\right)\left(\sqrt{0.2209} +\sqrt{0.1681}\right)}\\ =\frac{\left(\sqrt{0.2209} +\sqrt{0.1681}\right)^{2}}{\left(\sqrt{0.2209}\right)^{2} -\left(\sqrt{0.1681}\right)^{2}}\\ =\frac{0.2209+0.1681+2\sqrt{0.2209\times 0.1681}}{0.2209-0.1681}\\ =\frac{0.389+2\sqrt{0.03713329}}{0.0528}\\ =\frac{0.389+0.1927}{0.0528}\\ =\frac{0.2316}{0.0528}\\ =\frac{2316}{528}\\ =4.38 \end{array}$

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更新于: 2022年10月10日

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