Simplify \(\sqrt{150}\) to \(5\sqrt{6}\).
\[5\sqrt{6}+\sqrt{216}-\sqrt{600}=y\sqrt{6f}-{y}^{p}r\imath mepr\imath me\]
Simplify \(\sqrt{216}\) to \(6\sqrt{6}\).
\[5\sqrt{6}+6\sqrt{6}-\sqrt{600}=y\sqrt{6f}-{y}^{p}r\imath mepr\imath me\]
Simplify \(\sqrt{600}\) to \(10\sqrt{6}\).
\[5\sqrt{6}+6\sqrt{6}-10\sqrt{6}=y\sqrt{6f}-{y}^{p}r\imath mepr\imath me\]
Use Product Rule : \({x}^{a}{x}^{b}={x}^{a+b}\).
\[5\sqrt{6}+6\sqrt{6}-10\sqrt{6}=y\sqrt{6f}-{y}^{p}{r}^{2}{\imath }^{2}{m}^{2}{e}^{2}p\]
Use Square Rule : \({i}^{2}=-1\).
\[5\sqrt{6}+6\sqrt{6}-10\sqrt{6}=y\sqrt{6f}-{y}^{p}{r}^{2}\times -1\times {m}^{2}{e}^{2}p\]
Simplify \({y}^{p}{r}^{2}\times -1\times {m}^{2}{e}^{2}p\) to \({y}^{p}{r}^{2}\times -{m}^{2}{e}^{2}p\).
\[5\sqrt{6}+6\sqrt{6}-10\sqrt{6}=y\sqrt{6f}-{y}^{p}{r}^{2}\times -{m}^{2}{e}^{2}p\]
Regroup terms.
\[5\sqrt{6}+6\sqrt{6}-10\sqrt{6}=y\sqrt{6f}-(-{e}^{2}{y}^{p}{r}^{2}{m}^{2}p)\]
Simplify \(5\sqrt{6}+6\sqrt{6}-10\sqrt{6}\) to \(\sqrt{6}\).
\[\sqrt{6}=y\sqrt{6f}-(-{e}^{2}{y}^{p}{r}^{2}{m}^{2}p)\]
Remove parentheses.
\[\sqrt{6}=y\sqrt{6f}+{e}^{2}{y}^{p}{r}^{2}{m}^{2}p\]
Separate terms with roots from terms without roots.
\[\sqrt{6}-{e}^{2}{y}^{p}{r}^{2}{m}^{2}p=y\sqrt{6f}\]
Square both sides.
\[6-2{e}^{2}\sqrt{6}{y}^{p}{r}^{2}{m}^{2}p+{e}^{4}{y}^{2p}{r}^{4}{m}^{4}{p}^{2}=6{y}^{2}f\]
Divide both sides by \(6\).
\[\frac{6-2{e}^{2}\sqrt{6}{y}^{p}{r}^{2}{m}^{2}p+{e}^{4}{y}^{2p}{r}^{4}{m}^{4}{p}^{2}}{6}={y}^{2}f\]
Simplify \(\frac{6-2{e}^{2}\sqrt{6}{y}^{p}{r}^{2}{m}^{2}p+{e}^{4}{y}^{2p}{r}^{4}{m}^{4}{p}^{2}}{6}\) to \(1+\frac{-2{e}^{2}\sqrt{6}{y}^{p}{r}^{2}{m}^{2}p+{e}^{4}{y}^{2p}{r}^{4}{m}^{4}{p}^{2}}{6}\).
\[1+\frac{-2{e}^{2}\sqrt{6}{y}^{p}{r}^{2}{m}^{2}p+{e}^{4}{y}^{2p}{r}^{4}{m}^{4}{p}^{2}}{6}={y}^{2}f\]
Factor out the common term \({e}^{2}{r}^{2}{m}^{2}p\).
\[1+\frac{-{e}^{2}{r}^{2}{m}^{2}p(2\sqrt{6}{y}^{p}-{e}^{2}{y}^{2p}{r}^{2}{m}^{2}p)}{6}={y}^{2}f\]
Regroup terms.
\[1+\frac{-{e}^{2}(2\sqrt{6}{y}^{p}-{e}^{2}{y}^{2p}{r}^{2}{m}^{2}p){r}^{2}{m}^{2}p}{6}={y}^{2}f\]
Move the negative sign to the left.
\[1-\frac{{e}^{2}(2\sqrt{6}{y}^{p}-{e}^{2}{y}^{2p}{r}^{2}{m}^{2}p){r}^{2}{m}^{2}p}{6}={y}^{2}f\]
Divide both sides by \({y}^{2}\).
\[\frac{1-\frac{{e}^{2}(2\sqrt{6}{y}^{p}-{e}^{2}{y}^{2p}{r}^{2}{m}^{2}p){r}^{2}{m}^{2}p}{6}}{{y}^{2}}=f\]
Switch sides.
\[f=\frac{1-\frac{{e}^{2}(2\sqrt{6}{y}^{p}-{e}^{2}{y}^{2p}{r}^{2}{m}^{2}p){r}^{2}{m}^{2}p}{6}}{{y}^{2}}\]
f=(1-(e^2*(2*sqrt(6)*y^p-e^2*y^(2*p)*r^2*m^2*p)*r^2*m^2*p)/6)/y^2
