Question

rationalize the denominator 3+2 * root 2

Answer 1

Dear student
$$\begin{gathered} \mathrm{Assuming}\mathrm{the}\mathrm{question}\mathrm{is}\mathrm{rationalize}:\frac{1}{3+2\sqrt{2}} \\ \mathrm{We}\mathrm{have} \\ \frac{1}{3+2\sqrt{2}}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}} \\ =\frac{3-2\sqrt{2}}{3^2-{\left(2\sqrt{2}\right)}^2} \\ =\frac{3-2\sqrt{2}}{9-8} \\ =3-2\sqrt{2} \\ \mathrm{Note}: \\ {\mathrm{a}}^2-{\mathrm{b}}^2=\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}-\mathrm{b}\right) \end{gathered}$$
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