Question

$$\sqrt{ 2 \frac{ 1 }{ 4 } }$$

Answer

sqrt(2)/2

Solution


Simplify  \(2\times \frac{1}{4}\)  to  \(\frac{2}{4}\).
\[\sqrt{\frac{2}{4}}\]
Simplify  \(\frac{2}{4}\)  to  \(\frac{1}{2}\).
\[\sqrt{\frac{1}{2}}\]
Simplify.
\[\frac{\sqrt{1}}{\sqrt{2}}\]
Simplify  \(\sqrt{1}\)  to  \(1\).
\[\frac{1}{\sqrt{2}}\]
Rationalize the denominator: \(\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}\).
\[\frac{\sqrt{2}}{2}\]

Decimal Form: 0.707107