Question

$$470 \sqrt{ \frac{ 1 }{ 470 \times 1 \times } }$$

Answer

sqrt(470*)

Solution


Simplify  \(470\times 1\)  to  \(470\).
\[470\sqrt{\frac{1}{470}}\]
Simplify  \(\sqrt{\frac{1}{470}}\)  to  \(\frac{\sqrt{1}}{\sqrt{470}}\).
\[470\times \frac{\sqrt{1}}{\sqrt{470}}\]
Simplify  \(\sqrt{1}\)  to  \(1\).
\[470\times \frac{1}{\sqrt{470}}\]
Rationalize the denominator: \(470\times \frac{1}{\sqrt{470}} \cdot \frac{\sqrt{470}}{\sqrt{470}}=\frac{470\sqrt{470}}{470}\).
\[\frac{470\sqrt{470}}{470}\]
Cancel \(470\).
\[\sqrt{470}\]