Question

$$\sqrt{ \frac{ 96 }{ 9 } }$$

Answer

(4*sqrt(6))/3

Solution


Simplify  \(\frac{96}{9}\)  to  \(\frac{32}{3}\).
\[\sqrt{\frac{32}{3}}\]
Simplify.
\[\frac{\sqrt{32}}{\sqrt{3}}\]
Simplify  \(\sqrt{32}\)  to  \(4\sqrt{2}\).
\[\frac{4\sqrt{2}}{\sqrt{3}}\]
Rationalize the denominator: \(\frac{4\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{2}\sqrt{3}}{3}\).
\[\frac{4\sqrt{2}\sqrt{3}}{3}\]
Simplify  \(4\sqrt{2}\sqrt{3}\)  to  \(4\sqrt{6}\).
\[\frac{4\sqrt{6}}{3}\]

Decimal Form: 3.265986