Question

$$\sqrt{ \frac{ 1 }{ 9 } - \frac{ 4 }{ 15 } + \frac{ 4 }{ 25 } }$$

Answer

1/15

Solution


Simplify  \(\frac{1}{9}-\frac{4}{15}+\frac{4}{25}\)  to  \(\frac{1}{225}\).
\[\sqrt{\frac{1}{225}}\]
Simplify.
\[\frac{\sqrt{1}}{\sqrt{225}}\]
Simplify  \(\sqrt{1}\)  to  \(1\).
\[\frac{1}{\sqrt{225}}\]
Since \(15\times 15=225\), the square root of \(225\) is \(15\).
\[\frac{1}{15}\]

Decimal Form: 0.066667