Question

$$\sqrt{3\times\sqrt{3\times\sqrt{3\times\sqrt{9}}}=fah??$$

Answer

f=(9*sqrt(3))/(a*h)

Solution


Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[\sqrt{3}\sqrt{3}\sqrt{3}\times 3=fah\]
Simplify  \(\sqrt{3}\sqrt{3}\sqrt{3}\times 3\)  to  \(3\sqrt{3\times 3\times 3}\).
\[3\sqrt{3\times 3\times 3}=fah\]
Simplify  \(3\times 3\)  to  \(9\).
\[3\sqrt{9\times 3}=fah\]
Simplify  \(9\times 3\)  to  \(27\).
\[3\sqrt{27}=fah\]
Simplify  \(\sqrt{27}\)  to  \(3\sqrt{3}\).
\[3\times 3\sqrt{3}=fah\]
Simplify  \(3\times 3\sqrt{3}\)  to  \(9\sqrt{3}\).
\[9\sqrt{3}=fah\]
Divide both sides by \(a\).
\[\frac{9\sqrt{3}}{a}=fh\]
Divide both sides by \(h\).
\[\frac{\frac{9\sqrt{3}}{a}}{h}=f\]
Simplify  \(\frac{\frac{9\sqrt{3}}{a}}{h}\)  to  \(\frac{9\sqrt{3}}{ah}\).
\[\frac{9\sqrt{3}}{ah}=f\]
Switch sides.
\[f=\frac{9\sqrt{3}}{ah}\]