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

To do :

We have to simplify \( : \frac{\sqrt{0.2209}+\sqrt{0.1681}}{\sqrt{0.2209}-\sqrt{0.1681}} \).

Solution :

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

To factorize the denominator, multiply and divide by $\sqrt{0.2209}-\sqrt{0.1681}$.

Therefore,

$ \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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Updated on: 10-Oct-2022

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