Question

$$find=\sqrt{2}+\sqrt{3}(2-\sqrt{3})$$

Answer

f=-((sqrt(2)+sqrt(3)*(2-sqrt(3)))*IM)/(n*d)

Solution


Divide both sides by \(\imath \).
\[fnd=\frac{\sqrt{2}+\sqrt{3}(2-\sqrt{3})}{\imath }\]
Rationalize the denominator: \(\frac{\sqrt{2}+\sqrt{3}(2-\sqrt{3})}{\imath } \cdot \frac{\imath }{\imath }=-(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath \).
\[fnd=-(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath \]
Divide both sides by \(n\).
\[fd=-\frac{(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath }{n}\]
Divide both sides by \(d\).
\[f=-\frac{\frac{(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath }{n}}{d}\]
Simplify  \(\frac{\frac{(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath }{n}}{d}\)  to  \(\frac{(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath }{nd}\).
\[f=-\frac{(\sqrt{2}+\sqrt{3}(2-\sqrt{3}))\imath }{nd}\]